Game Theory and Its Applications to Takeovers [1 ed.] 1527561046, 9781527561045

Table of contents :
Dedication
Contents
Foreword
Acknowledgements
1 Introduction
2 Takeovers-State of the Art & Noncooperative Games
3 The Theory of Corporate Takeover Bids: A Subgame Perfect Approach
4 Modelling Real Estate Takeovers: A Corporate Finance Approach
5 Takeovers and Merger of Building Societies
6 Conclusions
Appendix A: Mathematical Notations
Appendix B-1: Glossary of TermsThe Language of Corporate Takeovers
Appendix B-2: Glossary of TermsThe Language of the Game Theory
Appendix C
References
Endnotes

Citation preview

Game Theory and Its Applications to Takeovers

Game Theory and Its Applications to Takeovers By

Suresh Deman

Game Theory and Its Applications to Takeovers By Suresh Deman This book first published 2021 Cambridge Scholars Publishing Lady Stephenson Library, Newcastle upon Tyne, NE6 2PA, UK British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Copyright © 2021 by Suresh Deman All rights for this book reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the copyright owner. ISBN (10): 1-5275-6104-6 ISBN (13): 978-1-5275-6104-5

This book is dedicated to my parents in their loving memory, who inspired me to go into higher education, although they never got a chance to have their own education.

CONTENTS

Foreword .................................................................................................... ix Acknowledgements ................................................................................... xii Chapter 1 ..................................................................................................... 1 Introduction Chapter 2 ..................................................................................................... 4 Takeovers-State of the Art & Noncooperative Games 2.1 Noncooperative Game Theory & Takeovers ................................... 4 2.2 The Game Theoretic Applications ................................................... 6 2.3 Historical Background ..................................................................... 7 2.4 Issues Surrounding Corporate Takeovers ...................................... 11 2.5 The Market for Corporate Control ................................................. 15 2.6 Real Estate Development ............................................................... 20 2.7 Building Societies or Cooperative Banks ...................................... 23 2.8 Initial Public Offerings (IPOS) ...................................................... 24 2.9 Dividends Signalling ...................................................................... 25 2.10 Capital Structure .......................................................................... 27 2.11 Capital Structure as Precommitment ............................................ 30 2.12 Financial Intermediation-An Incentive Design ............................ 31 2.13 Assets Pricing .............................................................................. 32 2.14 Credit Markets & Bank Failures .................................................. 33 2.15 Run on the Bank & Financial Crises ............................................ 35 2.16 Conclusions .................................................................................. 38 Chapter 3 ................................................................................................... 39 The Theory of Corporate Takeover Bids: A Subgame Perfect Approach 3.1 An Overview of Grossman and Hart Model .................................. 39 3.2 Formal Model and Mathematical Notations................................... 41 3.3 The Equilibrium Strategies and Outcomes of Takeover Bids ........ 42 3.4 Ex-Ante Efficiency and the Optimal Choice of Dilution ............... 51 3.5 Corporate Takeovers, Regulations and Economic Efficiency ........ 52 3.6 Corporate Takeovers and Dynamics of Tender Offers .................. 53

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Contents

Chapter 4 ................................................................................................... 56 Modelling Real Estate Takeovers: A Corporate Finance Approach 4.1.Introduction .................................................................................... 56 4.2. Historical Background .................................................................. 59 4.3. Real Estate and the Eminent Domain............................................ 61 4.4. Modelling Real Estate Takeovers ................................................. 63 4.5 Formal Model and Notation ........................................................... 64 4.6 The Equilibrium Strategies and Outcomes of Takeover Ds ........... 65 4.7 Ex-Ante Efficiency and Optimal Choice of Eminent Domain ....... 75 4.8 Conclusion and Direction for Future Research .............................. 78 Chapter 5 ................................................................................................... 80 Takeovers and Merger of Building Societies 5.1 Introductions and Historical Background ...................................... 80 5.2 Motivations Behind Mergers of Building Societies ....................... 83 5.3 Inter-Sectoral Takeover Mechanism .............................................. 88 5.4 Lloyds Bank V C & G - Performance ............................................ 90 5.5 Inter-Sectoral Merger - Search for Theories .................................. 91 5.6 Lloyds Bank’s Offer and Response of C & G Members ................ 93 5.7 Formal Model based on Corporate Takeovers ............................... 95 5.8 Introduction of a Prime Rate .......................................................... 99 Chapter 6 ................................................................................................. 101 Conclusions Appendix A ............................................................................................. 106 Mathematical Notations Appendix B-1 .......................................................................................... 108 Glossary of Terms The Language of Corporate Takeovers Appendix B-2 .......................................................................................... 112 Glossary of Terms The Language of the Game Theory Appendix C.............................................................................................. 114 References ............................................................................................... 115 Endnotes .................................................................................................. 125

FOREWORD

Professor Suresh Deman makes an excellent contribution with his book “Game Theory and Its Application to Takeovers” and resolves some of the controversies existing in the economic profession. In particular, the author critically analyses the theory put forward by Grossman and Hart (1980) in their seminal paper, published in Bell Journal, and provides a satisfactory explanation to the takeover problems. The beauty of the ‘Game Theory’ is not so much in its eloquent mathematical modelling but in its application to real-world problems. In Chapter 2, the author identifies game theory applications in different areas and connects modern concepts, like ‘Common knowledge’ to Confucius’s dialogue with his teacher, “I know that you know, you know that I know, I know that you know that I know, and so on” (Last Emperor of China)”. In fact, this chapter, combined with definitions of corporate terminology in an appendix at the end of the book, is very useful for communicating the complex ideas to practitioners and policy makers in simple language. In Chapter 3, the author summaries Grossman and Hart’s game theoretic approach and deals with the issues of takeovers and the free-rider problem. A raider wanting to take over a firm, where shareholders are dissatisfied with the incumbent management, offers higher than the prevailing market price to shareholders to entice them to sell their shares. However, even this strategy may fail as each shareholder, before selling his shares, hoping that share prices will rise further, waits for other shareholders to sell their shares, leading to a situation where no sale of shares takes place. This behaviour, known as the free-rider problem, ensures failure of the takeover bid due to the assumption of continuum of shareholders in which no individual shareholder can change the success of the tender offer because only the aggregate play is observed. As a solution to this problem, Grossman and Hart argued that a mechanism evolved whereby, if the raider were to be successful, he would be permitted to dilute the value of the shares withheld. This would facilitate the takeover bid, resulting in an outcome beneficial to all shareholders. However, their results are based on somewhat restrictive

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Foreword

assumptions of a game with a continuum of players and extreme scenarios, in which either shareholders sell or do not sell, known as pure strategy equilibriums. Dr. Deman’s major contribution lies in his assertion that even without resorting to dilution, a takeover bid may succeed, assuming there are a finite number of players, with no residual problem of the disappearance of information due to even a very small change in the aggregate play whenever a player deviates, but remains perfectly observable. Hence, deviations can be rewarded or penalised regardless of the number of players. A random risk element is introduced in the model. Arguing that this is a case of complete but imperfect information, shareholders do not know with certainty what would be the value of their shares after the takeover. This uncertainty reduces the expected value of their shares and they agree to sell at lower prices. The author applies this logic to another important area of urban renewal in Chapter 4. He applies corporate finance and game theoretic models in that chapter to real estate and urban renewal problems. He shows that the urban land market is also beset with free-rider problems. If a developer wishes to purchase a dilapidated housing area, each homeowner, before selling his house, waits for other homeowners to sell so that he could benefit from improved prices. Here, the developer would succeed only if the local authorities intervene. The author shows that it is not necessary. Dr Deman argues that homeowners have dissimilar expectations regarding the gains from urban renewal and thus, do not operate as a block of holdouts. The concept of mixed strategy equilibrium is a limit of equilibriums where each player’s payoffs are randomly perturbed by a small amount that is unobservable to his opponent. In Chapter 5, Dr Deman extends the application of game theory to another important area—the disappearance of building societies in the UK. Again, using game theoretic models, he explains how mergers of building societies with the high street banks in the UK led to the disappearance of building societies, giving suboptimal outcomes to the building societies, and defeating the very purpose for which building societies were created.

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In conclusion, the author has done a superb job in analysing the various factors affecting the takeover process and its impact on welfare by using game theoretic concepts. His work makes a valuable contribution to the theory and application of game theory in explaining economic phenomena, and it will be a good addition to the subject matter.

Prof C R Rao, Sc.D. (Cantab), F.R.S. Former, Director Indian Statistical Institute Honorary Fellow of King’s College Eberly Chair Statistics, PSU RSS Guy Medal, National Medal of Science (US) Wilks Memorial Award Padma Vibhushan National Science Award, India

ACKNOWLEDGEMENTS

I wish to thank a number of my colleagues and friends who have given me moral support in completing my research. Over the last twenty years of my academic career, I have published a number of research articles in refereed journals and presented my research to the international community. I am indebted to Professor C.R. Rao who supported me all the way through my pursuit of knowledge, making helpful comments and also helping me a great deal finding jobs all over the world. I benefited from comments from referees of professional journals. Professors Edward Green, Spyros Vassilakis, Reuben Slesinger, Robert Aumann, Reinhard Selton, John Nash and others offered critical and helpful comments on earlier drafts of my papers, which I have included in my thesis. I am particularly grateful to Professors Nick Wilson, Saburo Saito, TK Krishna Kumar, Arjit Mukherjee, Vrajainder Upadhayay and Amresh Hanchate for their patient and enthusiastic reading of the entire thesis. Their vigorous comments have greatly improved the clarity and quality of presentation. I believe, without their support, I would not have completed my thesis. Last but not the least, my wife Jenny deserves my most profound thanks for her patience and understanding during all the time that I was perspiring in front of my laptop, desperately awaiting glorious ideas, amusing words, or a turn of phrase, and at the same time watching my toddler daughter, Samantha, who was learning to walk, speak and repeat every word that was uttered.

CHAPTER 1 INTRODUCTION

In the last decade, hostile takeovers have become prevalent in the corporate world and have generated a great deal of controversy in the world of economics and in society at large. The so-called “Chicago School” of Antitrust has offered the intellectual reasoning for a considerable loosening of antitrust laws, which, particularly in the recent past, has gained the attention of both economists and journalists. The fourth wave of hostile takeovers in the US and UK has led many leaders of the business community and the public to question the desirability of takeover activity. During the 1980s, economists and finance researchers made strenuous efforts to understand the factors which result in hostile takeovers. Factors identified have included: disciplining managers; rationalisation of industries; realising economic efficiency; exploitation of economies of scale; synergy gains; the acquisition of market power; diversification; the acquisition of undervalued assets; vertical integration; managerial self-interests; “the urge to merge”, etc. Of course, not documented in the above list are the more idiosyncratic reasons, which tend to apply on a case-by-case basis. Economists tend to ignore these case specific factors in their search for stylised facts and general principles to explain broad takeover patterns and trends. There is therefore a twin focus to this study of takeovers. The first is to identify important game-theoretic studies that involve the theoretical underpinnings and rationale behind the hostile takeover process. The second focus of this study is to apply a game theoretic theoretical model of the corporate takeover to other sectors of the economy in order to understand the process of takeover and mergers across two institutional systems, namely, the US and the UK. In pursuit of these aims, this study will endeavour to marry both economic theory and application, in that an application only makes good sense if it is grounded within a sound theoretical framework.

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Chapter 1

In this study, I propose to re-examine some of the earlier work of Grossman & Hart (1980a) on corporate takeovers. They strongly argued in favour of exclusionary devices as being socially desirable and necessary for successful takeovers, arguing that they lead to a Pareto improvement outcome. There has been widespread concern in the business community since the 1970s over the various provisions of “dilution” under the Securities law. The existing Law of Securities and Exchange Commission in the US allows the raider to “dilute” the corporation’s shares to some extent, if the takeover bid is successful, to prevent minority shareholders from receiving all of the gains in the value of their shares. Opponents of dilution say that such provisions are tantamount to legitimised stealing from those shareholders who have not earlier tendered their shares to the raider in response to a tender offer. This analysis implies that raids can succeed with this mechanism if the raider’s offer to buy shares from the shareholders is coercive. Grossman & Hart (1980) offered arguments in the defence of “dilution” which are widely accepted. They show that the prospect of “dilution” can induce shareholders to sell their shares to the raider, and the long-term cost of “dilution” may be more than offset by the gains due to improvement in the management. In Chapter 2, I focus on the importance of game theory, and review developments in the application of game theory to takeover and merger activities in various sectors of the economy. Deman (1989, 1991, 1994, 2000) reconsiders Grossman and Hart’s (1980) paper under complete and imperfect information. The paper identifies the main shortcomings of Grossman and Hart’s model and addresses them using a subgame perfect approach. More general results are presented on the basis of an extended model. I show the existence of mixed strategy symmetric equilibriums with or without the dilution, and that the prisoner’s dilemma and the free-rider problem can be overcome in a takeover process. Furthermore, I identify two kinds of equilibriums: one is a ‘separating equilibriums’ in mixed strategies in which each type of raider behaves differently and the shareholders randomise their payoffs. The raider of a high-type will not offer a low price because such an offer would more than likely not succeed, and he would lose the potential gain on his initial shares. A less plausible kind of equilibrium is ‘pooling equilibriums’ in which different types of raiders behave in the same way. However, pooling equilibriums are ruled out by the reasonable ‘out-of-equilibrium belief’ that the price offer will signal the

Introduction

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raider’s type. In that case, a low-type raider could profitably differentiate himself from the pooling equilibrium by offering a low price, and the shareholder would accept his offer. In fact, a model of finitely many players under noise gives the same results as the continuum of players’ model in which any individual player’s decision does not affect the success of the bid. In Chapter 3, I present a game theoretic model of takeovers to re-examine Grossman & Hart’s earlier work on takeovers, state propositions, and also discuss the implications of the main results. In Chapter 4, I suggest an application of corporate finance-game-theoretic models to real estate takeovers. For example, when considering the problem of the developer negotiating with landowners, a model of finitely many owners appears to be much more realistic. It is well known that takeovers do occur with positive probabilities in models with finitely many players. This result holds independently whether or not these finitely many owners believe that they have an impact on the success of the sale as pointed out by Shleifer and Vishny (1986), Bagnoli and Lipman (1988), Bebchuk (1989), and Deman (1991, 1994, 1999, 2000). An analytical structure and formal model of the merger of building societies has been presented in Chapter 5. In this section, I also explore the theoretical underpinning and motivation underlying takeover and merger activities and ex-ante efficiency. Conclusions and directions for future research are discussed in Chapter 6. A Glossary of terms of the language of takeovers and game theory is presented in Appendix B, which is widely accepted. See Deman (1997).

CHAPTER 2 TAKEOVERS-STATE OF THE ART & NONCOOPERATIVE GAMES

2.1 Noncooperative Game Theory & Takeovers The Game theory begins with the publications of von Neumann (1928) and von Neumann and Morgenstern (1944); however, its roots can be traced back to the pioneering study of Cournot (1838), Model of Duopoly. The classical origin is dated even earlier, and one can find a flavour of non-sequential learning games and best response in well-known sayings of Confucius translated into the military writing of Mao Zedong and, more popularly, in fortune cookies in Chinese restaurants: “Consistency is the virtue of fools and wise people change their minds as they grow wiser.” “If the enemy is sharp, you become sharper; and if the enemy is sharper you become the sharpest.”

Similarly, the formulation of common knowledge is not obvious but commonly believed to be due to Aumann (1976). However, one can also sense the notion of common knowledge in Confucius’s dialogue with his teacher, which runs as follows: “I know that you know, you know that I know, I know that you know that I know, and so on” (See, last Emperor of China).

Economists began to realise the importance of limitation on the information possessed by individuals in understanding economic behaviour because such limitation induces agents to change their behaviour. The standard assumptions of perfect competition, that individuals are mere price-takers, are no longer relevant. Rather, the strategic interactions have potentially profound implications on the behaviour of agents in the decision-making process, by altering the behaviour in the rest of the market. Game theory is well-suited for modelling takeovers because of the importance of

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information, and its ability to include a number of sharply delineated sequences of moves and events. Precommitment and information transformation are the two pillars of modern game theory. Thus, the stylised facts and rationality of game theory may apply better to markets for corporate control than to markets for vegetables in developing countries. Finance as a field has developed in its own right, incorporating the element of uncertainty into asset pricing and the recognition of the failure of classical analysis to explain many aspects of corporate finance. The First generation of game theoretic models revolutionised finance, but much remains to be explained. Game theoretic methods keep developing, and we believe that some developments, involving richer informational models, are especially relevant for finance. Although Keynes (1936) and Hicks (1939) took account of risk by adding a risk premium to the interest rate, there was no systematic theory underlying the risk premium. The main theoretical development, eventually leading to such a theory, was an axiomatic approach to choice under uncertainty, due to von Neumann and Morgenstern (1947). Their notion of expected utility, developed originally for use in game theory, underlies the vast majority of theories of asset pricing. In the business world, the power of game theory as a management tool rests on reasonably comprehensive assumptions that are embedded in the rules of the game. Players can experiment with different solutions and concepts to problems that are intrinsically unsolvable. In other words, there are no unique solutions to the problems. The analysis of the results can be used for greater insights into the real problems the game simulates. In a game involving a large number of players, using a wide range of strategies, it is possible to identify strategies that do better than others, even if there is no unique correct strategy at all. Aumann (1987) defines game theory as like an umbrella or ‘unified field’ theory for the rational side of the social sciences, where ‘social’ is interpreted broadly, to include human as well as non-human players (computers, animals, plants). In game theory, the prisoner’s dilemma is commonly used for describing certain real-world problems. The central characteristics of a prisoner’s dilemma are an array of benefits and detriments associated with the alternative strategy, so that the dominant individual strategy is not to cooperate. The parties do not cooperate in pursuit of individual self-interest. This strategy yields less than optimal results.

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Chapter 2

There is a wide range of applications of Game theory in finance. However, in this chapter, I will focus on the application of a few that are relevant to my thesis in order to convey the sense of game theory. The typical example of models is signalling through information transmission in corporate takeovers, the capital structure as a commitment, and incentive design for financial intermediation. There is other literature in finance, for example, market microstructure, executive compensation, dividends and stock repurchases, external financing, debt signalling, etc., in which game theory has also been applied.

2.2 The Game Theoretic Applications The standard economics and finance theories failed to provide satisfactory explanations for observed phenomena, which led to a search for theories using new techniques. Chiefly, this was true in corporate finance where the existing models were so clearly unsatisfactory due to complexities of data due, in turn, to high volume and frequency. Game theory has provided a methodology that has led to insights into many previously unexplained phenomena by allowing asymmetric information and strategic interaction to be incorporated into the analysis. We start with a discussion of the use of game theory in corporate finance where, to date, it has been most successfully applied. Game theory is well suited for modelling takeovers because of the importance of information, and its ability to include a number of sharply delineated sequences of moves and events. Precommitment and information transformation are the two pillars of modern game theory. Thus, the stylised facts and rationality of game theory may apply better to markets for corporate control than to markets for vegetables in developing countries. It is worth exploring how the first generation of game theoretic models tackled those problems. In the corporate world, the power of game theory as a management tool rests on reasonably comprehensive assumptions that are embedded in the rules of the game. Players can experiment with different concepts and solutions to problems that are intrinsically unsolvable. In other words, there are no unique solutions to the problems. The analysis of the results can be used for greater insights into the real problems the game simulates.

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2.3 Historical Background The takeover of corporations is not a new phenomenon. In fact, it has been in existence since the corporate set-up started. However, prior to the 1960s, mergers and acquisitions were widespread in the market for corporate control. Economic historians, like Lamoreaux (1985), Sismic (1984), Greer (1980), and Nelson (1959) identified three, or perhaps four, major merger waves from 1893 to 1980. The US corporations affected over 3,000 mergers in the first wave of mergers (1893–1904). The Sherman Antitrust Act of 1890, which outlawed the collusion in corporations, but not mergers, was ended by the Supreme Court’s Northern Trust decision, in 1984. The second wave (1926–30) was characterised by horizontal mergers, resulting in oligopolies in which a few large firms dominated an industry, and was ended by the collapse of securities market associated with The Great Depression. The third wave (the mid-1950s to 1970) is associated with conglomerate mergers, in which corporations diversified their activities through mergers, driven by the Celler-Kefauver Merger Act, 1950. The merger wave ended in 1970, with the decline in the stock market, which eroded the equity base for leveraged purchases. The fourth major wave of acquisitions in the 1980s, perhaps beginning at the end of the 1970s, is characterised by the inter-firm tender offers. Mergers and acquisitions of a number of companies and transactions in billions of dollars during the second and third waves are given in Figure 1. Austin and Fishman (1970) pointed out in a study that tender offers did not become a popular mechanism for transferring corporate control until the 1960s. The tender offer mechanism is explained in Figure 2. According to Austin and Fishman, only nine inter-firms tender offers were made between 1956 and 1960. In fact, prior to the 1960s, the tender offer was used exclusively to acquire shares in the issuer’s repurchase programme; the so-called intrafirm tender offers. In contrast, 238 tender offers were made over the next eight years, 1960–1967. One can infer from the available data that the increase in the separation of ownership and corporate control in large corporations led to the development of the inter-firm tender offer as an important vehicle for transferring corporate control. A recent report of the Securities and Exchange Commission (SEC) reveals that between 1981–1984, a total of 228 successful tender offers of all kinds were made.

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Chapter 2

Tender offers are distinguished from mergers in that the former bids are made directly to shareholders to buy some or all of their shares for a specified price during a specified time. Thus, unlike merger proposals, which require the approval of the managers (directors) of the target corporation, many tender offers for takeovers are made and successfully executed over the objections of the target management. The word “takeover” is used as a generic term to refer to any acquisition through a tender offer. Economic analysis has identified two broad classes of takeovers. The first one in economics literature is known as disciplinary takeovers. The purpose of such takeovers seems to be to correct the non-value-maximising practices of the managers of the target corporations.

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The second class of takeovers can be characterised as synergistic. The motivating force behind them is the possibility of realising benefits from combining the businesses of two corporations. Synergistic gains can accrue to the corporation from the consolidation of research and development labs or of market networks, etc. The intuition behind corporate takeovers is represented in Figure 3.

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Chapter 2

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In the literature, the first type of takeovers is called hostile takeovers and the second type is called friendly takeovers. There are major analytical differences between these two classes of takeovers. Formal takeover models by Baron (1983), Png (1984), Fishman (1985), Giammarino and Henkel (1986), etc., represent the class of friendly takeovers, whereas Grossman and Hart (1980), Bradley and Kim (1985), Shleifer and Vishny (1986), Bagnoli and Lipman (1986), Bebchuk (1989), Holmstorm and Nalebuf (1992), Hirshleifer and Titman (1990), Deman (1991, 1994), etc., belong to the class of models representing hostile takeovers. There is a sharp contrast within the latter category, however. For example, Grossman & Hart (1980) consider a case of a continuum of owners, whereas Kovenock (1984), Shleifer and Vishny (1986), Bagnoli & Lipman (1988), Hirshleifer and Titman (1990), Deman (1991, 1994), etc., have considered finitely many owners. An important difference between these two classes of models is that the former assumes that the firm behaves as a unit, since an offer is made directly to management, hence, the free-rider problem does not arise. On the other hand, in hostile takeovers, since the offer is made directly to shareholders, the free-rider problem plays a major role because shareholders individually make their tendering decisions. Furthermore, the value of the firm, conditional on the takeover bid’s failure, is an important decision variable in friendly takeover bids. In contrast, competing for takeover bids in hostile takeover contests is relevant only if they are made prior to the expiration of the initial tender offer. For a given tender offer, and the ex-post value of the firm conditional on the success of the offer, the tendering decisions of small shareholders are not affected by whether or not a better offer was forthcoming. Hence, the possibility of competing bids can have a different impact on takeover contests depending on whether or not the bids are friendly or hostile.

2.4 Issues Surrounding Corporate Takeovers Fishman (1986) and Deman (1994) identified the existence of two main theories of corporate takeovers. The first theory hypothesises that takeovers exist due to a lack of complete state-contingent claims markets. The main argument can be summarised briefly as follows: if complete state-contingent claims markets exist, then shareholders’ valuations of any state-distribution of returns are identical (because of one price for every state-contingent claim) hence, they agree on the value-maximising production plan. However, in the absence of complete-state contingent claims markets, any

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Chapter 2

change in technologies (i.e., change in state-distribution of payoffs) is not, in general, valued identically by all shareholders. Thus, a majority support for such change in plans may be lacking. A takeover is a contingent contract, which enables a simultaneous change in technologies and portfolio holdings. This line of argument, with the exception of Giammarino and Henkel (1986), does not seem to be either popular or useful, which is judged by the paucity of literature on such models. The second line of argument of the theory on takeovers, which has gained the attention of economists and journalists, especially over the last decade or so, is the “agency theory” argument. According to this theory, the firm’s managers maximise their own interests, which may not coincide with shareholders’ interests (lavish consumption of perks or perquisites, overpayment to employees and suppliers, inefficient management, etc.). However, if any shareholder monitors the managers, all the shareholders reap the benefits and the individual shareholder does not get commensurate returns from his investment in monitoring managers. Thus, it does not pay any individual shareholder to monitor the firm. Under these circumstances, however, there may be an incentive for some outsider to take over the firm, improve its management and sell its share of the firm at a higher value. Such a takeover may result in the loss of utility to the target’s manager (loss of salary, being branded inefficient, etc.). Hence, the threat of takeover motivates the managers to work harder in the interests of the shareholders. The second line of reasoning of the theory of takeovers by the inter-firm tender offers has raised two theoretical issues. Firstly, the well-known free-rider problem is associated with the takeover mechanism. Manne (1965) argued that if a firm is inefficiently run by the incumbent management, then a raider, if he is more efficient than the current management, can offer more than the status-quo value of the shares, buy out the firm and run it more efficiently. This improvement in management will raise the value of the firm so that the raider can earn a profit by reselling it. Grossman and Hart (1980) have shown that atomistic shareholders have an incentive to free ride on the improvements affected by the raider. The free-rider problem becomes obvious where there is a continuum of shareholders, since no individual shareholder can change the success of the tender offer. Assuming shareholders have rational expectations if the takeover is going to succeed, no shareholder will sell unless he is offered a price, at least to the post-takeover value of his share. Consequently, the raider cannot purchase a share unless he pays at least what the share is worth to him if the raid is successful. If he does so, then even ignoring any costs of making a takeover bid, a raider cannot earn profits by taking over the firm.

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The second issue is the application of the Prisoner’s Dilemma to target shareholders. The argument suggests that target shareholders, if left to their own devices, will respond to a tender offer in a manner contrary to their best interests, not because they lack wisdom, but because of the “special dynamics,” of the tender offer process. It is argued that, as in the game theorist’s prisoner’s dilemma, it may be in the best interests of an individual shareholder to tender in response to an offer, even if the shareholders as a group would be better off if no one tendered. Management discretion to block an offer then rescues shareholders from the unfortunate result of pursuing their individual, as opposed to their collective, self-interest. For shareholders who face a prisoner’s dilemma, even if they require a champion to protect their interests under such circumstances, it is arguable whether the target management is a likely candidate for that role. Since management has an inevitable clash of interest with respect to the hostile takeover tender offers, one cannot tell whether their opposition results from circumstances that give rise to a genuine prisoner’s dilemma or from self-interest to protect their jobs. Many of those who call for increased government regulations of the tender offer process draw on these two arguments to make their case for policy recommendation. Grossman and Hart (1980a) addressed the first theoretical issue concerning the free-rider problem. Their argument runs like this: it is commonly believed that a loosely held corporation that is not being run in the interests of its shareholders will be vulnerable to a takeover bid. They show that this is false, since shareholders can free ride on the raider’s improvement of the corporation, thereby seriously limiting the raider’s profit. They strongly advocate exclusionary devices, which can be built into the corporate Charter for making the takeover mechanism successful. They offer arguments which are widely accepted in defence of the dilution. They also analyse the free-rider problem using the charter of the corporation and ensure that it is privately and socially optimal under alternative assumptions of competition and a monopoly market for corporate control. Under the assumption of a continuum of agents, since shareholders will not sell their shares for any price less than the expected value to them after the takeover, the presence of dilution creates the difference between the status-quo value and the potential value of the shares to the raider. Hence, this mechanism has the effect of lowering the acquisition price, and allows the raider to deprive minority shareholders of receiving the improvement in the value of their shares produced by the takeover mechanism.

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Chapter 2

Furthermore, they show that the prospects of dilution can induce shareholders to sell their shares to the raider, and the long-term cost of dilution may be more than offset by the gains due to an improvement in the management. The existing laws of the Securities and Exchange Commission allow the raider to dilute the corporation’s share to some extent, if the takeover bid is successful. Although actual corporate shareholders do not specify a monetary limit on dilution, they do specify the extent to which minority shareholders are protected from dilution. Grossman and Hart (1980a) expressed concern over the effect of implicitly requiring the disclosure of any intention to dilute the rights of shareholders who do not tender. Their analysis suggests that government policy on takeover bids following the Williams Act of 1968, may have had certain undesirable consequences by creating obstacles in the takeover process. Somewhat similar changes were also incorporated in the UK. Bradley and Kim (1985) addressed the second issue. In their paper, they examined the evolution of the offer as a takeover device. The tender offer had been used for years by investors who wanted to acquire a block of a firm’s stock in a short period of time. However, it was not until the significant increase in the public holdings of corporate stocks, in the 1960s, that the tender offer device became a popular vehicle to take control of a firm and replace its management. In other words, the tender offer is an effective takeover mechanism, only if there are sufficient shares outstanding and trading in public markets. Using this same logic, they develop a model that implies that, as the number of shares held by management increases, there is greater likelihood that a takeover bid will take the form of a negotiated merger instead of a public tender offer. In their paper, they show that in a sample of 112 successful tender offers, the median percentage of shares held by insiders is 6.4%, and in a sample of 192 successful mergers median insiders holding is 14.1%. They also find that the maximum insider holding for the tender offer sample is 38%, whereas in the merger sample the maximum is 99%. They also show that the tender offer is an efficient takeover mechanism, since it can be constructed to solve both the free-rider problem of the bidder and the prisoner’s dilemma of the target stockholders. Therefore, as argued above, the two-tier tender offer must be outlawed because of its coercive nature.

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There are two other important papers, Bagnoli and Lipman (1988) and Hirshleifer and Titman (1990), which address somewhat similar issues and have shown some other equilibrium in the game. An earlier paper by Kovenock (1984) also shows mixed strategy sub-game equilibrium as shown by Bagnoli and Lipman, but he does not consider the optimal strategy of the raider. However, their models are somewhat different in the following respects. First, the assumptions in the above papers are quite different from that of Grossman and Hart. They, in fact, relaxed the assumptions of atomistic shareholders in their models. Bagnoli and Lipman allow shareholders to own more than one share of stock, and Hirshleifer and Titman deal with the large shareholder case and use different assumptions in the game of finite shareholders. Secondly, both these papers fall short of conditions under which mixed strategy equilibrium will exist. Thirdly, the profit equation in the Bagnoli and Lipman paper appears somewhat arbitrary and results in meticulous expression. Fourthly, they do not address the limitations of the welfare implications of Grossman and Hart’s model. My approach is to take virtually the same assumptions as Grossman and Hart and show that mixed strategy equilibriums do not exist, which was overlooked in their paper. However, the mixed strategy equilibriums exist if the dilution is not infinite (100%). Hence, there are limiting equilibriums and not the equilibriums in the limit (i.e. as the dilution approaches infinity, pure strategy symmetric equilibriums are realised, because if anyone deviates from the pure strategy, the value of his or her shares will be zero after the takeover), which establishes some parallel with the concept of limit pricing in Milgrom and Roberts (1982). In the following section, I briefly describe the Grossman and Hart (1980a) model, operating in the background to the ongoing debate on corporate takeovers. I also discuss the growing importance of game theory and its application in critically reviewing some of the earlier work on takeovers.

2.5. The Market for Corporate Control Manne (1965) was the first to develop the notion of the market for corporate control. He argued that in order to utilise the resources efficiently, it is necessary that firms are run by the most competent managers. It was suggested that the most efficient way this could be realised in modern capitalist economies is through the market for corporate control. There are many ways in which this operates, including tender offers, mergers, buyouts, proxy fights, etc.

Chapter 2

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The traditional theory of finance, with its assumptions of symmetric information and perfectly competitive and frictionless capital markets, had very little to offer in providing insights into the market for corporate control. In fact, the huge premiums over initial stock market valuations paid for targets appeared to be at variance with market efficiency and posed something of a puzzle. It was not until the beginning of game theoretic concepts and techniques that much progress was made in this area. Grossman and Hart’s (1980) paper provides a formal theoretical model of the takeovers process and generated a great deal of controversy and interest in the economics profession. They explain a particular free-rider problem using a game-theoretic model with a continuum of players. Suppose that under status-quo management, a corporation has value v and if the raider can improve the target’s value by x, then its potential value is v + x. If the takeover bid is conditional and v < p < (v + x) i.e. price p is below the potential value, no shareholder will sell, even though they would jointly profit. If the shareholder will only be willing to trade at a price equal to the post-takeover value, and shareholders free ride on the value-improvement, then the raider will not be able to recover even the cost of making a tender offer. The shareholders are in a prisoner’s dilemma and if the takeover bid is going to be successful then a holdout is better, and no worse if it fails. Hence, tendering is not a dominant strategy. So, every shareholder holds out and in Nash-Equilibrium, the takeover will never occur. Grossman and Hart (1980a) strongly argued in favour of exclusionary devices, known as the dilution factor by suggesting that the raider is allowed to dilute the value of the minority shareholder if the raid is successful. TAKEOVER GAME Shareholder S1 Shareholder 2

40, 40

25, 50

50, 25

37.5, 37.5

Matrix 1 An analysis of the free-rider problem in Bradley and Kim (1985) demonstrates that a necessary condition for a tender offer to be successful is that it should be front-end loaded. This condition should hold regardless of whether the tender offer is a partial or two-tier offer. This is another application of the prisoner’s dilemma, for example, Matrix-1. Suppose two shareholders equally own a corporation and its underlying value is $80. The raider makes a tender offer in which >50% shares will be purchased at a

Takeovers-State of the Art & Noncooperative Games

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price of $50 and the remaining 50% shares tendered. If both tender, the share will be purchased on pro-rata basis. Under these conditions, tendering is a dominant strategy, even though all the shareholders would be better off refusing to sell. It is argued that the two-tier tender offers must be outlawed because of their coercive nature. However, Bradley and Kim argue that there is no reason to outlaw two-tier offers because they help reallocate corporate resources to their highest valued use. This allows for greater flexibility in financing takeover activity by reducing the amount of cash that a potential raider must accumulate to pursue an acquisition. They further suggest that the potential for competition among raiders and a dominating intra-firm tender offer could solve the prisoner’s dilemma. There is a growing focus in the literature on problems of achieving equilibrium in markets where agents are imperfectly or asymmetrically informed. The information failures can lead to capital rationing in loan and credit markets. It has been argued that an alternative German system of corporate governance, now better known as “insiders”, provides an interesting example, although recent global crises have limited its scope. However, this approach points out the importance of institutional factors, which affect the way information is distributed among the agents and argues that it can have an important bearing on the allocative and technical efficiency. Unfortunately, like the theory of complete contingent-claim markets, very little work has been done in this direction. Fishman (1986) develops a model of the takeover bidding process. The model can be described as a form of auction in which a bidder can acquire costly information after the bidding has begun. Implications concerning the interrelationships between bidders’ and targets’ profits, bidders’ initial offers, single and multiple bidder contests, and the effects of takeover legislation are developed. Additionally, the model provides a rationale for bidders to make high premium (“pre-emptive”) initial bids, rather than making low initial bids and raising them if there is competition. Shleifer and Vishny (1986) point out that if the raider is a large shareholder and, if permitted to profit from secretly purchasing D proportion of shares prior to the tender offer, then the free-rider problem can be solved, even without dilution. The tender offer can be profitable because, the raider can profit on his own shares even if he offers p > (v + x) and loses out on the tendered shares. Their model also sheds light on the following questions: Under what circumstances will we observe a tender offer as opposed to a proxy fight or an internal management shake-up? How strong are the forces

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pushing toward increasing concentration of ownership of a diffusely held firm? Why do corporate and personal investors commonly hold stock in the same firm, despite their disparate tax preferences? However, the empirical evidence is inconsistent with this argument. Bradley, Desai, and Kim (1988) found that the majority of bidders own no shares prior to the tender offer. Hirshleifer and Png (1989) present a model of corporate acquisitions in which initially uninformed bidders must incur costs to learn their (independent) valuations of a potential takeover target. The first bidder makes either a pre-emptive bid that will deter the second bidder from investigating, or a lower bid that will induce the second bidder to investigate, and possibly compete. They show that the expected price of the target may be higher when the first bidder makes a deterring bid than when there is competitive bidding. Hence, by weakening the first bidder’s incentive to choose a pre-emptive bid, regulatory and management policies to assist competing bidders may reduce both the expected takeover price and social welfare. Bebchuk (1989) focused on takeover bids for which the outcome can be predicted in advance with certainty. Grossman and Hart (1980) established the proposition, which subsequent work accepted, that successful bids must be made at or above the expected value of minority shares. This proposition provided the basis for Grossman and Hart’s identification of a free-rider problem and became a major premise for the analysis of takeovers. This paper shows that this important proposition does not always hold once we drop the assumption that the only successful bids are those whose success could have been predicted with certainty. In particular, it is shown that any unconditional bid that is below the expected value of minority shares, but above the independent targets per share value, will succeed with a positive probability. The bidder’s expected payoff from such a bid (not counting the transaction costs of making the bid) is always positive, and bidders might elect to make such bids. These results have implications for the nature of the free-rider problem and for the operation of takeovers. In particular, it has been shown that, when the raider can increase the value of a target’s assets, the raider might elect to bid even if no dilution of minority shares is possible and it holds no initial stake in the target. Hirshleifer and Titman (1990) relax the assumptions of Shleifer and Vishny (1986) and present a model of tender offers in which the bid perfectly reveals the bidder’s private information about the size of the value

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improvement that can be generated by a takeover. They argued that bidders with greater improvements would offer a higher premium to ensure that sufficient shares are tendered to obtain control. The model relates announcement date of returns and takeover success or failure to the amount bid, the initial shareholdings of the bidder, number of shares the bidder attempts to purchase, the dilution of minority shareholders, and managerial opposition. They show that managerial defensive measures, either by raising the incentive to bid high or by decreasing the asymmetry of information about the improvement, will sometimes increase the probability of the offer succeeding. They explain why offers succeed sometimes, but not always. Following Milgrom and Roberts (1982), nature moves first and chooses the raider’s “type” to be x  (0, ൉] and the raider offers a premium of x for each of D proportion of shares. Each of the continuums of shareholders decides whether to sell, or not to sell, his shares. If over (0.5-D) shareholders accept the tender offer, the payoffs are p for those who accept and (v + x) for those that refuse. Otherwise, all payoffs are zero. Kyle and Vila (1991) investigated a model of takeovers in which “noise trading” provides camouflage and makes it possible for a large corporate outsider to purchase enough shares at favourable prices so that takeovers become profitable. Although the model accommodates the possibility of dilution, as in Grossman and Hart 1980), and a large incumbent shareholder, as in Shleifer and Vishny 1986), neither dilution nor a large incumbent shareholder is necessary for costly takeovers to be profitable. Noise trading tends to encourage costly takeovers that otherwise would not occur and discourage beneficial takeovers that otherwise would occur. Holmstorm and Nalebuf (1992) also re-examine the free-rider problem, as discussed by Grossman and Hart. They focus on two different ways to model the continuum of shareholders: there may be a large number of shareholders and a large number of shares. A failure of the raider to capture any of the surpluses depends, critically, on the assumption of equal and indivisible shareholdings, i.e. one-share-per-shareholder model. In contrast, they have shown that once shareholdings are large and potentially unequal, a raider may appropriate some, or even all, the efficiency gains from his takeover. In conclusion, the free-rider problem does not prevent the takeover process when shareholdings are divisible. Another puzzle that has been documented in the empirical literature on takeovers is the fact that bidding in takeover contests occurs through several large jumps rather than many small ones. Jennings and Mazzeo (1993) found that a majority of the initial bid premiums were over 20% of the

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market value of the target 10 days before the offer was being made. This evidence conflicts with the standard solution of the English auction strategy. This suggests there should be many small bid increments. Deman (1994, 2000) re-examines Grossman & Hart’s earlier work on corporate takeovers and addresses three main shortcomings of their theory. First, their theory implies that in the “Nash equilibrium” either all shareholders will decide to sell any or all of their shares, or they will all refuse to sell to the raider. Hence, they look only at the pure strategy equilibriums. Secondly, it appears as though the free-rider problem in the extreme cases of pure strategy equilibriums will not develop because everyone sells his or her share in the equilibrium, and no minority shareholders will be left to free ride. On the other hand, if the raid fails and no one sells, then there does not arise any question of dilution either. I show mixed-strategy equilibriums, which Grossman & Hart overlooked in their earlier work. Thirdly, Grossman and Hart claim that their theory rules out the possibilities of takeovers by the inefficient raider in which the shareholders who tender their shares are worse off than they would otherwise have been with the incumbent management. It appears from the model that their argument is based on rather arbitrary assumptions.

2.6. Real Estate Development A search of the literature reveals the existence of a few game theoretic models developed by Kaneko (1983), Gerber (1985), Eckart 1985), and Asami (1988), Asami and Teraki (1990) to address the problem of site assembly and land development subject to indivisibility. However, with the exception of Eckart, all other models ignore the very important economic realities of players holding rational expectations, and their strategic interaction in the urban renewal game. Furthermore, none of these models address issues related to market efficiency, which are crucial for studying real estate takeover for urban renewal. Deman and Wen (1994) use a two-stage formulation of a simple three-person game and show the existence of socially desirable pure strategy symmetric equilibriums, which depend on the assumptions of atomistic ownership and complete indivisibility of the redevelopment project. The model employed is not descriptive of actual processes. Rather, it is an application of a Subgame Perfect Approach to provide evidence in favour of how the market for development purchases should be organised to realise Pareto efficiency by applying democratic rules. Had such an approach been used by the State Governments, there would have been less controversy surrounding land

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acquisition in West Bengal, Uttar Pradesh, Karnataka, etc. The interdependence of urban property value has, of course, long been recognised. People consider not only the quality of services associated with a particular dwelling unit, but also the attractiveness of the neighbourhood when deciding to buy or rent an urban property. There are possibly five key dimensions of a neighbourhood’s quality that are considered: i) adequate parking and recreational facilities; ii) good schooling; iii) sanitation services; iv) quality of surrounding housing units; and v) absence of crime. Two main kinds of market imperfections may exist. The first would result from the external effects of one property on the owner of another as discussed by Davis O. A. and A. B. Whinston (1964). The second one is related to site assembly. These problems have not been adequately addressed in the literature. One can employ a simple 2x2 matrix to explain how interdependence can cause slum equilibriums or preponderance of urban blight. Consider a two-player game (w.l.o.g.) with two adjacent properties, called Owner I and Owner II. Let us assume each property gives return I & II on investment. Now each owner is trying to determine whether to make the additional investment for redevelopment or to improve the value of the property. The additional investment in property will, of course, increase the return to each owner, but the decision of Owner I would influence Owner II. A normal-form game can summarise the owners facing the dilemma in Matrix-2 as follows: Landowner I

Landowner II

I

NI

I

.08, .08

.04, .10

NI

.10, .04

.05, .05

Matrix 2 The entry in I row and I column shows average returns of 8% to each owner from the redevelopment of property if both Owners I & II decide to invest, i.e., “Invest, Invest.” Similarly, II row and II column show entries for

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average returns when both owners decide just the opposite, i.e., “Not Invest, Not Invest.” In the economics literature, such a situation is characterised as slum equilibriums. The remaining two entries in the matrix are symmetric, which represent the situation when one owner decides to invest but the other does not invest, i.e., “Invest, Not Invest.” This scenario is a little bit more complicated. It is assumed that the externalities include both economies and diseconomies. Let Owner II consider first to invest then Owner I assumed to derive benefits from Owner II’s investment as the redevelopment contributes something to improving the neighbourhood. The better neighbourhood may include, but not be limited to, the better quality of amenities surrounding housing units, such as off-street parking, street lightings, garbage collection, crime watch, sanitation services, better schooling, recreational facilities, etc. Thus, the owner can increase his returns to 10% by way of free-riding on the investment of Owner II who can realise only 4% total returns, since his renters also consider the ill-effect of the Owner I’s presence in the neighbourhood. By symmetry, the effect of Owner I, considering investing first, will be similar. However, these symmetrical situations are sub-optimal, hence, unstable equilibriums. Since the publication of Grossman & Hart’s (1980) work on takeovers, a number of papers have been published identifying the shortcomings of their work, but failed to provide any useful application of Grossman & Hart’s theory. Broadly speaking, there are two classes of papers in the literature on corporate takeovers. Fishman (1986) and Deman (1994) provide a useful analysis and insight on the subject. The first categories of papers rely upon a continuum of player assumption, for example, Grossman & Hart (1980) and others. The second class of papers focuses on the games of finitely many players. For example, papers by Kovenock (1984), Shleifer and Vishny (1986), Bagnoli and Lipman (1988), Hirshleifer and Titman (1990), Deman (1991, 1994), Holmstorm and Nelebuff (1992), Harrington and Prokop (1993), and Fluck (1993) have considered finitely many players in the game. The basic distinction between Grossman & Hart’s above paper and the others is the assumption of a continuum of players and atomistic shareholders. Why should this matter? Briefly, with a continuum of players’ assumption, the paradox is caused by the following “disappearance of information”, because only the aggregate play is observed. Hence, the individual deviation cannot be met by rewards and punishments. In a finite number of players’ game, there is a change in the aggregate play whenever a player deviates. The change may be very small, but perfectly observable. Therefore, deviations can be rewarded or punished regardless of the number

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of players. Hence, the results are straightforward—that takeovers will occur with positive probability in models with finitely many players. Deman (1999) provides, not only a useful application of Grossman & Hart’s theory, but also extends their theory on takeovers. Using measure theory of a statistic, a formal mathematical structure to Grossman & Hart’s model is being set up. I look at a class of games to include both the continuum and finitely many homeowners to contrast the situation when the redevelopment project is indivisible and partially divisible. In pure strategy equilibrium, a redevelopment project requires all property in the target blocks to be economically feasible, which can be realised through purchase by secrecy.

2.7. Building Societies or Cooperative Banks Takeover and acquisition of corporations is a well-researched area. Much less research emphasis has been devoted to takeover activity within the general area of financial services, particularly the building society sector. In the UK the building society is a typical example of a financial mutual. Such a shortfall in research is especially problematic for building societies given the extensive level of merger and takeover activity within the sector. Between 1990 and 1994 the number of societies declined from 2,286 to 81, with much of this decline accounted for by intra-sectoral merger and takeover activity. It does, however, now seem that non-building societies (inter-sectoral activities) are becoming increasingly interested in building societies as takeover targets. The building societies being mutual companies are distinct from corporations by their orientation towards non-profit objectives. The common element is in both creating value, however, mutuals create value by selling services at the price above the cost of provision as opposed to the structure ownership claims. Although, Barnes, P. and J. C. Dodds (1981) Barnes (1985), Gough (1979, 1981), Thompson (1996, 1997) have done some empirical studies of mergers activities within the building society sector, these studies deal with intra-sectoral mergers and have not addressed efficiency issues in a general equilibrium framework. To the best of my knowledge, no one has attempted to apply a game-theoretic technique to the study of mergers and takeover of the building societies. In fact, most of the research carried out so far on building societies is primarily meant for practitioners. A computer literature search confirms this. Deman (2000) suggested a mechanism at par with sales of stocks of a corporation to organise market for development purchase. I also present an

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analysis of the voting behaviour of members of Cheltenham and Gloucester building society, and also characterise their equilibrium strategies in a game theoretic context, which gives rise to less than optimal results.

2.8 Initial Public Offerings (IPOS) In early 1960, the Securities and Exchange Commission (SEC) carried out a study of IPOs which revealed that initially short-run returns on the stocks were significantly positive. Logue (1973), Ibbotson (1975) and many other successive studies found somewhat similar results. Ibbotson and Ritter (1995), in a survey article, asserted this during the first day of trading, based on data for the period 1962–1992. These large returns on IPOs were one of the most glaring challenges to market efficiency for many years. The standard models of the 1960s and 1970s, based on the assumptions of symmetric information, were no longer consistent with this observation. Rock (1986) was the first paper to provide a persuasive explanation of this phenomenon. The under-pricing in this model occurs because of adverse selection. There are two types of buyers for the shares, namely, those informed and uninformed about the true value of the stocks. The informed type of buyers will only buy when the offering price p ” v (true value). This implies that the uninformed buyers will receive a high allocation of overpriced stocks, since they will be the only ones in the market when p > v (true value). Rock suggested that to induce the uninformed buyers to participate in the market, they must be compensated for the overpriced stock they ended up buying. One way of compensating uninformed buyers is that, on an average, stock are under-priced. Rock’s above suggestion provoked debate in the literature and led to many theories of under-pricing: (i) as a signal (Allen and Faulhaber (1989); Grinblatt and Hwang (1989) and Welch (1989); (ii) as a way to induce investors to truthfully reveal their valuations (Benveniste and Spindt (1989)); (iii) avoid lawsuits (Hughes and Thakor (1992)); and, among others, (iv) price stabilisation (Ruud (1993)). In addition to the short run under-pricing puzzle, IPOs involve another anomaly. Ritter (1991) documented significant long-run underperformance of newly-issued stocks. He found a cumulative average underperformance of about 15% from the offer price relative to the matching firm during the period 1975–1984, and an underperformance of around 15% from the offer price relative to adjusted return. In subsequent papers, Loughran (1993) and

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Loughran and Ritter (1995) confirmed this long-run underperformance of stocks. A number of theories have been advanced to explain long-run under-performance based on the behavioural approach. Miller (1977) argued that there will be a wide range of opinion concerning IPOs and the initial price will reflect the most optimistic opinion. As information becomes public through time, the most optimistic investors will gradually adjust their beliefs, and the price of the stock will fall. Shiller (1990) argues the IPOs market is subject to an ‘impresario’ effect. Investment banks will try to create the appearance of excess demand and this will lead to a high price, initially, but, subsequently, to underperformance. Finally, Ritter (1991) and Loughran and Ritter (1995) suggest that there are swings of investor sentiment in the IPO market, and firms use the “window of opportunity” created by overpricing to issue equity. Although IPOs cover a relatively small part of the financing activity they have received a great deal of attention in the finance literature. Perhaps, the reason for this is the extent to which under-pricing and overpricing represent a violation of market efficiency. It is interesting to observe that while game theoretic techniques have provided many explanations of under-pricing, they have not been utilised to explain overpricing. Instead, the explanations have relied on eliminating the assumption of rational behaviour on the part of investors.

2.9. Dividends Signalling The thorniest issue in finance has been what Black (1976) termed “the dividend puzzle”, as the main theoretical issue. Historically, firms are paid out about a half of their earnings as dividends. Many of these dividends were received by investors in high tax brackets who, on the margin, paid substantial amounts of taxes on them. In addition, Linter (1956), in a classic study, demonstrated that managers “smooth” dividends, in the sense that they are less variable than earnings. Fama and Babiak (1968) and many other authors have confirmed this finding. Miller and Modigliani (1961) suggested, in their original paper on dividends, that dividends might convey significant information about a firm’s prospects. However, this issue was not fully understood, and no progress was made until game theoretic techniques were applied to this issue. Bhattacharya’s (1979) model of dividends as a signal was one of the first papers in finance to apply the game theoretic techniques to address this

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issue, which evoked a large literature on dividends as signalling for firms’ prospects. Bhattacharya assumes asymmetry in information, wherein the managers have superior information about the profitability of their firm’s investment. Ex-ante, they can convey this information to the capital market by “committing” to a sufficiently large number of dividends. If ex-post the project is profitable these dividends can be paid from earnings without a problem. On the other hand, if the project is unprofitable then the firm has to raise external finance and incur a deadweight loss due to transaction costs. Therefore, the firm will only find it worthwhile to commit to a high level of dividends if, in fact, its prospects are bright. Subsequently, a few authors like Miller and Rock (1985) and John and Williams (1985), developed models which waived Bhattacharya’s assumptions of committing to a certain level of dividends, and where the deadweight transaction costs required to make the signal credible were plausible. In a seminal paper, Kumar (1988) identified one of the problems with signalling models of dividends which suggest that they will be paid to signal new information. In the model, there is no need to keep paying the owners, unless new information is continually flowing. In these circumstances, it is expected that the level of dividends should vary to reflect the new information. However, this feature of dividend signalling models is difficult to reconcile with smoothing. He developed a “coarse signalling” theory that is consistent with the fact that firms smooth dividends. In his model, firms within a range of productivity, all pay the same level of dividends to owners. When firms move outside this range they will alter their dividend level. Another problem in many dividend signalling models, including Kumar (1988), is that they do not explain why firms use dividends rather than share repurchases as signalling. It appears that in most signalling models’ dividends and share repurchases are essentially equivalent, except for the way that they are taxed. Although both involve transferring cash from the firm, the owner’s dividends are typically treated as ordinary income and taxed at high rates, whereas repurchases involve price appreciation being taxed at low capital gains rates. Ofer and Thakor (1987), Barclay and Smith (1988) and Brennan and Thakor (1990) suggest that repurchases have a disadvantage due to adverse selection problems, because the informed investors are able to bid for undervalued stocks and avoid overvalued ones. However, dividends do not suffer from this problem because they are issued on a pro-rata basis. It is fair to say that some progress on understanding the dividend puzzle has been

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made in the last decade. This is one of the areas of finance literature in which game theory has been somewhat successful.

2.10. Capital Structure Although a text version of the trade-off theory of capital structure had provided a better explanation of firms’ choices than the initial dividend models, the theory is not entirely satisfactory with the magnitudes of bankruptcy costs and interest tax shields, which seemed to be inconsistent with the observed capital structures. Application of game theoretic techniques in this area of finance has allowed it to advance significantly. Harris and Raviv (1991) survey the area. One of the first contributions in game theoretic applications was the signalling model. Ross (1977) develops a model whereby managers choose an appropriate level of debt, signalling the prospects of the firm to the capital markets. Debt acts as a signal because bankruptcy is costly. The basis of the reasoning is that a high debt firm with good prospects will only incur these costs occasionally, whilst a similarly levered firm with poor prospects will incur them quite often. Leland and Pyle (1977) considered a scenario where entrepreneurs use their retained share of ownership in a firm to signal its value type, “low” or “high”. Owners of high-value firms retain a higher share of the firm to signal their type that means they would not diversify as much as they would due to asymmetric information, which makes them unattractive for low-value firms to mimic. A couple of papers based on asymmetric information, which have influenced thinking, are Myers (1984) and Myers and Majluf (1984). If managers have superior information about the prospects of the firm than the capital markets, they will be unwilling to issue equity to finance investment projects if the equity is undervalued. Rather, they would prefer using equity when it is overvalued. Thus, equity is considered as a bad signal. Myers (1984) uses this reasoning to develop the “pecking-order” theory of financing. Managers have a choice between using equity to finance investment projects and less information-sensitive sources of funds, like retained earnings. In the pecking-order of sensitiveness, retained earnings are the most preferred, with debt coming next and finally, equity. A number of stylised facts concerning the effect of issuing different types of security on stock price and the financing choices of firms tend to support the results of these papers and the subsequent literature, such as Stein (1992) and Nyborg (1995). However, in order to derive these results, strong assumptions, such as Managers’ aversion to overwhelming bankruptcy, are often necessary.

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Moreover, Dybvig and Zender (1991) and others have stressed that the above models often assume suboptimal managerial incentive schemes. Further, they show that if managerial incentive schemes are chosen optimally the Modigliani and Miller irrelevance results can hold, even with asymmetric information. A second influential contribution to the literature on the capital structure using game theory concerns agency costs. Jensen and Meckling (1976) identified two kinds of agency problems in corporations: firstly, between equity-holders and bond-holders; and secondly, between equity-holders and managers. The first agency problem arises because the owners of a levered firm have an incentive to take risks; they receive the surplus when returns are high, but the bondholders bear the cost when default occurs. Diamond (1989) has addressed how reputation considerations can ameliorate the risk, shifting incentive when the time horizon is long. The second agency problem arises when equity holders are unable to fully control managers’ actions. This means managers have an incentive to pursue their self-interests, rather than those of the equity holders. Grossman and Hart (1982), Jensen (1986) and others have shown how debt can be used to overcome this problem. Myers (1977) pointed to a third agency problem. If there is a huge amount of outstanding debt, not backed by cash flows from the firm’s assets, what is known as “debt overhang,” equity holders may be reluctant to take on safe, profitable projects due to the bondholders’ claim to a large part of the cash flow. The agency cost perspective has also led to a series of influential papers by Hart and Moore (1989) and others on financial contracts. The authors use game theoretic techniques to highlight the role of possibilities of incomplete contracts in determining financial contracts, in particular, debt. Hart and Moore considered an entrepreneur wishing to raise funds to embark on a project. Both the entrepreneur and the outside investor observe the project’s payoffs at each date, but they cannot write explicit contracts based on these payoffs because third parties, such as courts, cannot observe them. The thrust of their study is the problem of how to provide an incentive for the entrepreneur to repay the debt. Among other things, they show that the optimal contract is a debt contract, and incentive to repay funds is one which provides the ability of the creditor to seize the entrepreneur’s assets.

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Subsequent developments in the literature include contributions by Hart and Moore (1994; 1998); Aghion and Bolton (1992); Berglof and von Thadden (1994); and von Thadden (1995). Hart (1995) contains an excellent chronology and exposition of many of the main ideas in this literature. Modigliani and Miller’s (1958) theory of capital structure is such that firms’ decisions of the product market are separated from the decisions of the financial market. In fact, the assumption of perfect competition in product markets can achieve this. In an oligopolistic model involving strategic interactions between firms in the product market, financial decisions are also likely to play a key role. Allen (1986), Brander and Lewis (1986) and Maksimovic (1986) and in subsequently developing literature, surveyed by Maksimovic (1995), have considered many different aspects of these interactions between product markets and financial markets. Allen (1986) considered a duopoly model, wherein a bankrupt firm is at a strategic disadvantage in choosing its investment because the bankruptcy process forces it to delay its decision. In a Stackelberg investment game, the bankrupt firm becomes a follower instead of a simultaneous mover as in a Nash–Cournot game. Brander and Lewis (1986) and Maksimovic (1986) have discussed the role of debt as a precommitment device in oligopoly models. By undertaking a large amount of debt, a firm effectively pre-commits to a higher level of output. Titman (1984) and Maksimovic and Titman (1993) have considered the strategic interaction between financial decisions and customers’ decisions. Titman (1984) looks at the effect of an increased probability of bankruptcy on product price, for example, the existence of difficulties obtaining spare parts and service should the firm cease to exist. Maksimovic and Titman (1993) considered the relationship between capital structure and a firm’s reputational incentives to maintain the high quality of a product. A significant component of the trade-off theory is the bankruptcy costs that impose a limit on the use of debt. An important issue concerns the nature of these bankruptcy costs. Haugen and Senbet (1978) argued that the extent of bankruptcy costs was limited because firms could simply renegotiate the terms of the debt and avoid bankruptcy, and its associated costs. The literature on strategic behaviour, around and within bankruptcy, leads to the use of game theoretic techniques extensively in Webb (1987); Giammarino (1988); Brown (1989); and surveyed in Senbet and Seward (1995). The analysis shows that Haugen and Senbet’s argument depended on the absence of frictions but with asymmetric information or other frictions, bankruptcy costs could occur in equilibrium.

30

Chapter 2

2.11. Capital Structure as Precommitment To address this, we consider a game under the assumption of Symmetric information. The main focus of the game is on commitment rather than on information transmission. In the game, each firm purposely risks bankruptcy to create a conflict of interest between debt and equity, which increases its aggressiveness in seeking market shares. The outcome is worse for the firms if they jointly avoid debt because debt lowers firms’ profits, whilst helping the firm that uses it as a commitment tool. This is another example of prisoner’s dilemma. We discuss the capital structure model, based on Brander and Lewis (1986), which has two firms in the same market. In the first move of the game, the firms simultaneously choose the debt level, and in the second they simultaneously choose output levels q1, q2. Nature then chooses the level of a random demand shock, (ș, 1) and profits are realised. It is assumed that firm i’s profit, Ȇi 2(qi,qj,3), is decreasing in qj and increasing in ș. When ș is large, a firm’s profits are higher, especially if it has chosen a high output level. If both firms choose zero debt, this is the Cournot game with certainty. The firms trade off the advantage of high output when ș is large against the disadvantage when ș is small. A firm with heavy debt, however, would go bankrupt if ș were low in any case, and if its shareholders do not care about the disadvantage of high output in the state, credit goes to limited liability. They do benefit from high output when ș is high, so heavy debt is an incentive for high output. Harris and Raviv (1988) focus on capital structure as an anti-takeover device because common stock carries voting rights whilst debt does not. The debt-equity decision may affect the outcome of corporate votes and thus, may partly determine the corporate resources. Thus, incumbent management can use short-term financial restructuring as tactics to influence the form of the takeover attempts and its outcome, assuming that managerial ability to identify good projects is unknown. In a subgame perfect reputational equilibrium, managers may choose too much safety compared to the shareholder’s optimum. If the firm issues debt, then this incentive aligns the manager’s interest with those of the shareholders and thus, reduces the agency costs of debt for them. This implies higher optimal leverage when the manager is motivated by his personal reputation than when he is not. This result is different from that of Harris and Raviv (1988).

Takeovers-State of the Art & Noncooperative Games

31

2.12. Financial Intermediation-An Incentive Design Financial intermediation is an area that Game theory has changed significantly. Gurley and Shaw (1960) show that traditionally the Banks and other intermediaries were regarded as ways of reducing transaction costs, although these banking models were not very rich. Diamond and Dybvig (1983) introduced Game theoretic techniques, which dramatically changed the literature on intermediation. They considered a simple model, where a bank provides insurance to depositors against liquidity shocks. Customers find out at the intermediate date whether they require liquidity then, or at the final date. Liquidating long-term assets at the intermediate date involves some cost. A deposit contract is based on first come, first served basis, i.e., where customers who withdraw first get the promised amount until resources are exhausted, after which nothing is received. This assumption results in two self-fulfilling equilibriums. The good equilibrium implies everybody believes only those who have liquidity needs at the intermediate date will withdraw their funds, and this outcome is optimal for both types of the depositors. In the bad equilibrium, everybody believes everybody else will withdraw. Given the first come, first served assumption, and that liquidating long-term assets is costly, it is optimal for early and late consumers to withdraw, and there is a run on the bank. Diamond and Dybvig argue that a provision of deposit insurance will eliminate the bad equilibrium. In most models, the players begin with Symmetric information, but they know that some players will later acquire an informational advantage over the others. The model that I am going to use here is an example of theory-based institutional economics. The purpose of this article is to show that: (a) an intermediary is useful only if there are many investors and many entrepreneurs; and (b) incentive contracts have economies of scales compared to monitoring. In Diamond’s (1984) model of financial intermediaries, M risk-neutral investors wish to finance N risk-neutral firms, each entrepreneur has a project that requires 1 unit in capital and yields Q level of output, where Q is initially unknown to anyone. If Q < 1, he genuinely cannot repay the investors, but the problem is that only he, not the investors, will observe Q, so they cannot validate his claim Q < 1. The investors must rely on one of two things to ensure the truth, namely, monitoring or incentive contract.

32

Chapter 2

Under the monitoring scheme, each investor incurs a cost, C, to observe Q, which makes it a contractible variable, on which payment can be made contingent. The entrepreneur suffers a dissipative punishment į10)x under the incentive contract if he repays x. The cost of monitoring is MC, whilst the expected cost of an incentive contract is E(į)11. In the absence of an intermediary, if E(į)12 < MC, the incentive contract is preferred. The underlying idea behind a financial intermediary is to eliminate redundancy by replacing M individual monitors with a single monitoring agency. The intermediary itself requires an incentive contract, at cost E(į)13. To justify its existence, it should spread this cost over many entrepreneurs. If N=1, the intermediary incurs a cost of C for monitoring and E(į)14 for its own incentive, whereas a direct investor-entrepreneur contract would cost only E(į)15. In the above scheme, while information is still symmetric, the institution assumes a particular form to avoid information problems by contracting. The main driving force behind the existence of financial intermediaries is the asymmetric information, which opens doors for a much wider application of game theory. Reputational issues on the part of borrowers become very important, and were first analysed by John and Nachman (1985) in a two-period model. They depicted, in sequential equilibrium, a problem in which agency debt can be decreased when compared with a single period model. Diamond (1989) uses a somewhat similar model, in which borrowers deal with banks over more than one period and have an incentive to build a reputation for repaying loans. This provides a partial improvement of the agency problem in one-shot games in which the borrower prefers riskier investment than the lender would like.

2.13. Assets Pricing Grossman and Stiglitz (1980) employed a nonstrategic concept of rational expectation equilibrium in an assets pricing model, incorporating asymmetric information. Although each market participant is assumed to learn from market prices, he/she still believes not to have influenced market prices. This approach helped address a number of novel issues, like ‘free riding’ in the acquisition of information. However, Dubey, Geanakoplos and Shubik (1987) identified a number of conceptual issues in reconciling asymmetric information with competitive analysis. This called for an explicitly strategic analysis in the model, motivating the recent literature on market microstructure.

Takeovers-State of the Art & Noncooperative Games

33

Strategic analysis entails the study of the process and outcomes of exchanging assets under explicit trading rules. The market microstructure literature seeks to explicitly model the process of price formation, usually in the context of financial markets, whereas general equilibrium theory simply assumes an abstract price formation mechanism. Kyle (1985) and Glosten and Milgrom (1985) make the initial important contributions and the subsequent literature that build on these two papers is sizable. O’Hara (1995) provides an excellent account of the literature. As I explained earlier, Kyle (1985) developed a model with a single risk-neutral market maker, a group of noise traders who buy or sell for exogenous reasons, such as liquidity needs, and a risk-neutral, informed trader. The market maker selects efficient prices and the noise traders simply submit orders. The informed trader chooses a quantity to maximise his expected profit. Glosten and Milgrom’s (1985) model also included a risk-neutral market maker, noise traders and informed traders. The main difference between Kyle and this model is that the quantities traded are fixed, and the focus is on setting the bid and ask prices rather than the quantity choice of the informed trader. In order to take into account the possibility that the trader may be informed and have a better estimate of the true value of the security, the market maker sets the bid-ask spread. As orders are received, the bid and ask prices change to reflect the possibility that the trader is informed. Also, the model is competitive in the sense that the market maker is constrained to make zero expected profits. Game theory has influenced a number of other asset-pricing topics, in addition to market microstructure. Cherian and Jarrow (1995) provide an excellent survey of the literature. Allen and Gale (1994) and Duffie and Rahi (1995) also use game theoretic techniques in some financial innovation models. However, these models are not as yet as fully developed as other areas in asset pricing. Pricing anomalies associated with P/E or P/B ratios, that have received a great deal of attention in recently, are intimately associated with accounting numbers. Again, game theoretic techniques seem likely to be a fruitful area of research, since these numbers are, to some extent, the outcome of strategic decisions analysis of these phenomena.

2.14. Credit Markets & Bank Failures Bryant’s (1980), and Diamond and Dybvig’s (1983) papers generated a large literature on bank runs and panics. Chari and Jagannathan (1988) considered the role of aggregate risk causing bank runs. Their paper

34

Chapter 2

focussed on a signal extraction problem, where part of the population observes a signal about the future returns on bank assets. Other part of the population must then try to deduce from observed withdrawals whether an unfavourable signal was received by this group, or whether liquidity needs happen to be high. Chari and Jagannathan show that panics occur, not only when the economic prospects are poor, but also when liquidity needs turn out to be high. Jacklin and Bhattacharya (1988) compared what happens with bank deposits to the impact when securities are held directly so runs are not possible. In their model, some depositors receive a signal about the risky investment. They show that it all depends on the characteristics of the risky investment whether either bank deposits or directly held securities can be optimal. Thakor (1996) and Allen and Gale (1999) have considered a comparison between two types of financial systems, bank-based and stock market-based. There are two other key papers, by Stiglitz and Weiss (1981) and Diamond (1984) in the literature on banking and intermediation, which helped transform the field. Stiglitz and Weiss developed an adverse selection model in which rationing credit is optimal, and Diamond (1984) gave a model of delegated monitoring, where banks have an incentive to monitor borrowers, otherwise, they will be unable to pay off depositors. Bhattacharya and Thakor (1993) provide a comprehensive account of the recent literature on banking. The credit market faces two main problems, namely, (i) moral hazard and (ii) adverse selection. The first problem arises because the lenders are unable to observe the borrower’s choice (i.e., their credit-worthiness) subconsciously, or ignore it in the expectation of higher interest (subprime lending), consciously. The second problem arises because of a great deal of heterogeneity among borrowers. Whilst the lenders might have a good idea about average characteristics of the pool of potential borrowers (know only the probability distribution of characteristics of borrowers), they may not have complete and perfect information about the individual characteristic of the borrowers (i.e. the actual type of borrowers). This leads to a problem of adverse selection, as the lenders are unable to distinguish between good borrowers and bad borrowers due to the asymmetry of information, which leads to two types of equilibrium, namely, Pooling & Separating Equilibriums. A typical real-world example of a bank loan is as follows: suppose two borrowers came to bank for an unsecured loan of $20,000 to put a down payment on purchase of a house. Normally, banks do not lend money to put a down payment on a mortgage, and can lend only 3–4 times of a borrower’s

Takeovers-State of the Art & Noncooperative Games

35

salary or income, depending on the practice and policy at the relevant time. One borrower is prepared to pay 10% interest and the other 100%. Which one should the lender chose?

2.15. Run on the Bank & Financial Crises A simple game could explain a bank’s failure and the dilemma of deepening financial crises. Let us assume there are two investors in a world of complete information. Each investor deposited a sum 100K (D) with a Bank, which it invested in deposits in a long-term project. If the Bank is forced to liquidate before maturity, a total of 160K (2r) can be recovered, whereas, 100K > 80K > 50K. If the Bank allows investors to reach maturity, Project payout is 120K (2R), where 120K > 100K. There are two dates at which Investor can make withdrawals: Date 1, before when the Bank’s Investment is not matured (run on the bank); and Date 2, when the Investment matures (no run on the bank). Strategies of players 1 & 2 are given by ȝ1 and ȝ2 respectively, and payoffs in a 2x2 matrix below: Next stage: we consider a scenario in which actions of player 1 are not perfectly observable to player 2 and vice versa. Hence, conjecture of players 1 and 2’s beliefs about each other are represented by ȝ12, ȝ21, respectively. Following Deman (2000), it is worth examining the outcome of the game, whether the players are better off if they randomise their strategies, rather than playing pure strategies of withdrawal to achieve a Pareto superior outcome. Player 1’s Strategy ȝ1

Player 1’s Strategy ȝ1

Player 2’s Strategy:ȝ2

W

NW

W

80,80

100,60

NW

60,100

Next stage

Payoff Matrix 1

Player 2’s Strategy:ȝ2

W

NW

W

80, 80

60k, 60k

NW

100, 60

120, 120

Payoff Matrix 2

Using backward induction to analyse the game, consider a Normal Form game at date 2. Clearly, the strategy to “withdraw” strictly dominates “don’t withdraw”, giving a unique Nash equilibrium with payoff (120, 120) [since no discounting]. Hence, there will be two pure strategy symmetric equilibriums: (1) both investors withdraw at Date 1 with payoffs (80, 80); and (2) both investors do not withdraw at date 1 but withdraw at Date 2 with

36

Chapter 2

payoff (120, 120). The outcomes of the above matrix 2 can be interpreted as follows: the first outcome is an inefficient outcome in which a run on the bank occurs as if the players are rational, and if player 1 believes that player 2 will withdraw then the best response of player 1 is to withdraw as well, although they would be better off had they waited until date 2. The bank run equilibrium is different from the prisoners’ dilemma in a very important respect. Although both games have Nash equilibrium which lead to socially inefficient outcome, in the case of prisoners’ dilemma this is a dominant strategy of players to give a unique Nash equilibrium. The presence of both, efficient and inefficient Nash equilibriums, make it difficult to predict runs on the bank. Hence, runs on the bank can occur as an equilibrium phenomenon. There are two sides to this phenomenon: (i) it is difficult to predict runs on the banks; (ii) it is possible to avoid runs on the banks if appropriate, timely steps are taken, monetary measures by Central Bank or fiscal measures by government, to induce mixed actions or strategies. Diamond and Dybvig (1983) developed a modern version of the financial crises, in that bank runs are self-fulfilling prophecies. They focus on pure strategies equilibrium and completely rule out mixed strategies equilibriums on the somewhat arbitrary basis that they are not economically meaningful. There are a few problems with their model. First, in the real world, only some banks fail, although recently the number of failed banks in the US has risen to 130 by the end of 2009. Secondly, it appears to follow that not everyone rushes to the bank to withdraw, unless the extent of panic become common knowledge and reaches the stage of the 1929 stock market crash and subsequent Great Depression. Thirdly, due to imperfect information, a number of agents do not even know that banks are failing. Fourthly, in their model they assumed that the management and the government will be either lame ducks or completely impotent. Finally, in the real world, even the healthy banks fail. Hence, their model lacks sound equilibrium basis of explanation. The mixed strategies can be introduced in the game if the players have complete, but imperfect, information about other players’ beliefs, and given by ȝ12 and ȝ21. It is improbable to assume that everyone will follow the irrational players in a panic, so late consumers can always imitate the early consumers, as suggested in Allen and Gale (1989a). Let us define a general form of a stochastic process over a probability space (:, E, 5), where : is the sample space, E some V-algebra and 5, a probability measure defined on E. Also define, ):: o R2, and the realisation of (c1, c2, ș = I(Z), where Z  :. I assume that c1, c2 are random

Takeovers-State of the Art & Noncooperative Games

37

variables with known distribution to at t = 0 and known to each player a t = 1. The consumers know c1 and c2 precisely at t = 1. The utility to consumers is defined as U (c1, c2; ș  R2++ o R1+ and their strategies are given by ȝk I(Z) ĺ [1, 0] at t = 1 and [0, 1] at t= 2. Consider a technology scenario in which there are 3 players, 1 Bank and 2 identical players, in period t = 0. There are three Dates t = 0, 1, 2, and a large number of continuum of consumers. Assume consumption takes place in two periods t = 1, 2. Initially, each player holds a single homogeneous good, i.e., endowment equal to 1 unit of consumption good. At t = 1 each player privately observed uninsurable risk of being type ȝnr or type ȝr (i.e., nr = non-risky and r = risky) and each care only about consumption in t = 1 and type 2 in period t = 2, respectively. To realise the homogeneity, let total amount of endowment in period be t = 0 is X, therefore, each player holds X/2 endowment. Players can store between t İ [0, 1] because the technology does at least as good, but better if held until t = 2. If ȝnr type obtains consumption goods at t = 1, he will store until t = 2 to consume them. Let player ȝnr receive goods for either consumption or storage represented by CT which is publicly observable. At t = 2 privately observed consumption of type ȝr player will be c1 + c2. Each player has a state-dependant utility function with private information: u1 (c1) U(c1, c2; ș =

with low prob pl

ȡ u2 (c1 + c2) with high prob ph

‫׊‬

μ1

‫׊‬

μ2

Assume that the utilities of players are given by U (c1, c2; ș and which is twice differential, increasing and strictly concave, and follows Inada conditions U’(0)= ’ and U’’ 0. Since all players are identical at t= 0, they can only write un-contingent contracts due to lack of public information on which to base the contingent. All players will engage in trade and each will invest his endowment in the production technology. Note, privately observed consumption of player of type ȝr at t = 2 will be (c1 + c2) because he stored c1 at t = 1. Since this becomes common knowledge, the state dependant variable for player ȝr will be equal to ȡX2 (c1 + c2), where ȡ is a discount factor. Let us assume a fraction of players, ȝnr type is N İ (0, 1) and conditional upon N, each player has an equal and independent chance of being in ȝnr. This assumption will be relaxed to make N random and at t = 1 each player

Chapter 2

38

knows his type, i.e., ȝnr or ȝr.

2.16 Conclusions Game theory has emerged as one of the most powerful techniques of analysis because, in the game, both players are actively trying to promote their own welfare in opposition to that of the opponent. It develops rational criteria for selecting a strategy, in which each player will uncompromisingly attempt to do as well as possible in relation to his opponent by giving the best response. However, game theory is often criticised on the grounds that it is sensitive to minor changes in the assumptions and lacks empirical verification. The existence of various equilibriums depends on what information is available to players, or who moves first. Deman (1987) basically identifies three criteria for a theory to be considered as useful if: (i) it is consistent with known facts; (ii) provides greater insights and understanding than earlier theories; and (iii) can be used for forecasting future trends, particularly under the conditions that differ from the past. The underlying assumption is that both theorists and empiricists have common objectives, namely, to describe, explain, relate, anticipate and evaluate phenomena, events and relationships crucial to decision-making, through theory construction and data collection. Unfortunately, crucial variables are hard to measure, but that does not attenuate their importance. As Rasmussen (1989) pointed out, the economist’s empirical work has dominated case-by-case verification, replacing the traditional regression-running. A theory’s sensitivity to assumptions is not a shortcoming. Rather, it is a contribution of the theory, pointing out the important role of what were once thought to be insignificant details of reality in the world. To blame game theory for any failure to predict, or for selfishness, is like blaming cardiology for heart disease. Failure of macroeconomic forecasts and the growing importance of the microeconomic theory of the firm have brought game theory to the forefront of economic decision-making. I conclude with a quote: “Just as marginalism is more than the application of calculus to old problems in economics, so game theory is as important for changing the agenda as for introducing new techniques.”

CHAPTER 3 THE THEORY OF CORPORATE TAKEOVER BIDS: A SUBGAME PERFECT APPROACH

3.1 An Overview of Grossman and Hart Model In this section, I will briefly discuss Grossman and Hart’s theoretical model on takeovers in the light of Chapter 2. Their argument runs as follows: a widely-held corporation that is not being run efficiently by the incumbent management is vulnerable to a takeover bid. Significant costs are associated with ensuring that managers act in the interest of the shareholders. Our survey of articles on takeovers indicated that virtually all of the theoretical models of takeovers are based on the assumption of atomistic shareholders. 1 The idea is similar to standard assumptions of competition, that there are a large number of small shareholders, none of whom can change the outcome of a takeover bid. Each shareholder in the corporation is so small that it is not in his interest to devote resources to overthrow an inefficient management. If any shareholder has a large enough incentive to devote resources to improve the corporation’s management, then all the shareholders benefit from his actions. Hence, shareholders face the problem of “unexcludability” of gains. It has been argued that facing these circumstances, a raider can, if he is more efficient than the current management, offer a tender price more than the current value of the share, taking over the corporation successfully. This improvement in management will eventually appreciate the value of the corporation, thereby enabling the raider to earn a profit by reselling the shares at a higher price. If the shareholders, individually, make a rational decision in response to a bid, in anticipation of a profit from the price appreciation after a successful raid, they may hold onto their shares rather than resell them. Hence, the takeover bid will not succeed and the inefficient management will be completely insulated from change. Such a situation results in a unique “Nash Equilibrium” solution and the tender offer fails. 2 Informal analyses of takeover models with a single raider and atomistic shareholders have suggested that the individual shareholder has an incentive to free ride on

40

Chapter 3

expected improvements to be affected by the raider. 3 Consequently, from the raider’s standpoint, a takeover bid may not be profitable because of this free-rider problem even though the incumbent management is not serving the best interests of the shareholders. Thus, the raider likewise faces the same sort of externality that any shareholder would face if he devoted resources to improving the corporation’s management. Hence, even in a corporation, “the public good is a public good”. 4 The government policy on takeover bids, since the Williams Act of 1968, has perhaps had certain undesirable consequences by making raids more difficult. 5 It would seem that a government should encourage raids rather than hampering them. To overcome the problem of free riding, certain exclusionary devices become necessary for successful takeovers. Grossman and Hart (1980a), on the basis of the free-rider issue, concluded that the takeovers are good because this mechanism succeeds in “internalising” the “externalities”. Grossman and Hart strongly advocated exclusionary devices as being socially desirable and necessary for successful takeovers, which leads to a Pareto improvement outcome. There is a widespread concern in the business community, since the 1970s, over the various provisions of “dilution” under the securities law. When a company issues new shares or when the stock options are exercised by employees, the number of shares in circulation increases, reducing the share of each stock holder (this is called dilution of shares). The existing laws of the Securities and Exchange Commission allow the raider to “dilute” the corporation’s shares to some extent (by issuing new shares), if the takeover bid is successful, to prevent minority shareholders from receiving all of the gains in the value of their shares. 6 Opponents of dilution say that such provisions are tantamount to legitimised stealing from those shareholders who have not earlier tendered their shares to the raider in response to a tender offer. This analysis implies that raids can succeed with this mechanism if the raider’s offer to buy shares from the shareholder is coercive. Grossman and Hart offered an argument in defence of “dilution”, which is widely accepted. Their argument is, since shareholders will not tender their shares for any tender offer of less than the expected ex-post takeover value of their shares, a divergence must be created between this value and the value of the shares to the raider. They call this divergence a “dilution”. 7 Such a provision has the effect of lowering the acquisition price through coercions, and permits the raider to exclude incumbent shareholders from the gains his takeover produces. The idea behind these mechanisms is that,

The Theory of Corporate Takeover Bids

41

“The only way to create a proper incentive for the production of a public good is to exclude non-payers from enjoying the benefits of the public goods”. 8 Furthermore, they show that the prospects of “dilution” can induce shareholders to sell their shares to the raider. In this analysis, the long-term cost of “dilution” may be more than offset by the gains due to improvement in the management. I believe there are three shortcomings in the Grossman and Hart theory of takeover bids. 9 First, there does not arise any free-rider problem in the cases of pure strategy equilibrium because if the takeover raid is successful, then all shareholders sell their shares and the raider does not have to deal with any minority shareholders in the equilibrium. On the other hand, if the raider is unsuccessful and no shareholders sell, then there is no question of dilution either. Second, the theory implies that in the “Nash Equilibrium”, either all shareholders will decide to tender their shares or else all will refuse the raider’s tender offer. Unfortunately, empirical studies do not seem to support such a takeover mechanism. Conversely, an empirical study by Aranow, Einhon, and Bernstein (1976) suggests a substantial and widespread incidence of non-tendering shares, irrespective of the nature of the tender offer. In fact, many actual takeovers are completed with only a fraction of the shares exchanged. Third, Grossman and Hart claim that their theory rules out the possibilities of takeovers by an inefficient raider in which the shareholders who tender their shares are worse off than they would otherwise have been with the incumbent management. It appears that their argument is based on rather arbitrary assumptions. In the present chapter, I would like to address these three issues. This chapter has been divided into six sections. Section 3.1 gives an overview of the Grossman and Hart Model; Section 3.2 states a formal model and mathematical notations; Section 3.3 evaluates the equilibrium strategies and outcomes of takeover bids; Section 3.4 examines welfare implications and the optimal choice of the dilution factor. In Section 3.5 I discuss corporate takeovers, regulations and economic efficiency. Dynamics of tender offer mechanism and the nature of takeover bids are presented in Section 3.6.

3.2 Formal Model and Mathematical Notations In this section, I state the formal assumptions of the atomistic shareholder model and also introduce mathematical notations. 10 Most of the assumptions are the same as those made by Grossman and Hart. I assume complete but imperfect information. I consider a two-stage game with k shareholders, each owning one share in the corporation. 11 Instead of assigning a market

42

Chapter 3

value to each share, I assume (without loss of generality, w.l.o.g., Q = 0) that the corporation’s value is Q = 0 when it is run by the incumbent management, and it is worth V, under the raider’s management. If a raider is more efficient than the current management, the potential value V will be greater than Q, i.e. V > Q. From this, each share of the corporation is worth Q/k and V/k to the shareholders under the current and raider’s management, respectively. I completely drop the management from our model, assuming that the managers are impotent and they do not use the defensive mechanism.12 I define a general form of a stochastic process over a probability space (:, E, 5) where : is the sample space, E some V-algebra and 5 a probability measure defined on E and C is the cost of achieving V. I also define ):: o R2, and the realisation of (v, c) = I(Z), where Z  :. I assume that V and C are random variables with known distribution to shareholders, i.e. common knowledge. The raider knows V precisely at the cost C. The price offered by the raider p is defined as: p: R2 o R+. Raider’s strategy is given by Vr (I(Z)). The shareholder’s strategy is given by Vk (P) which is defined as follows: Vk: R+ o[T, N], whereby tendering and non-tendering are represented by T & N respectively. The argument is the price offered by the raider Vr (I(Z)). Hence, a pure strategy of the shareholders is given by Vk: R+ o[1, 0] where 1 and 0 are for tending and non-tending, respectively. I define the mixed strategy for the shareholders: Xk: : o[1, 0] is independent and identically distributed, uniform and independent of ), and observed by the shareholders alone, i.e. a private lottery of the kth shareholder to determine whether this mixed strategy is just a private roulette. This is also represented by VMk: R+ x [1, 0]o[T, N]. Probability of tendering is defined as follows: 5[Vk=T/Vr=p] = 5[X{x|Vk (p, x) = T}] and is given by Vk(p).

3.3 The Equilibrium Strategies and Outcomes of Takeover Bids I follow Milgrom and Roberts (1982) and virtually make the same assumption as those made by Grossman and Hart in their paper (1980a). I assume that “nature” moves first and selects the values of the corporation V = [VL, VH] as value “low” and value “high”, according to a probability distribution Hi, given the shareholder’s subjective beliefs about the value of the corporation. Let V = [VL, VH] be the distribution that takes only two extreme values with positive probabilities. Since the shareholders are

The Theory of Corporate Takeover Bids

43

identical, they are going to have the same beliefs about the value of the corporation. Let 5L and 5H be the probabilities that V is low and V is high, respectively. A complete description of the extensive form game is given in Figure 5. Consider a simple two-stage game with one raider and two shareholders. Let the raider observes ) and makes a tender offer of price p, to two uninformed shareholders. To gain control over the corporation, the raider has to acquire at least one share. In the absence of special anti-takeover provisions in the charter of the corporation, a simple majority ownership is generally sufficient for controlling the corporation. Typically, a 50% majority is sufficient for gaining control of the corporation, i.e. (k+1)/2 shares are required and denoted by i=T. I start with a simple example; however, the results will hold for k shareholders. In the first stage of the game, the raider offers a price p based on his strategy Vr (I(Z)). Given the buying strategy of the raider, the second stage is the sub-game, played by the shareholders, in which each shareholder has two possible actions: tendering (T) or not tendering (N). I take all players to be risk-neutral. Hence, the expected payoff or utility to shareholder 1 is the sum of the expected value of his share if he tenders, and when he does not tender. I assume, for simplicity, if the takeover bid is unsuccessful, each share of the corporation is q and q = 0. 13 The expected payoffs of the shareholders 1 and 2 are given as follows: V1, V12) = U1(V V1(p). p + (1-V1(p)).V12(p) {1/2 [PL VL + (1-PL) VH -G]}

(1)

U2 (V2, V21) = V2(p). p + (1-V2(p)).V21(p) {1/2 [PL VL + (1-PL) VH -G]}

(2)

44

Chapter 3

The Theory of Corporate Takeover Bids

45

Where V12(p) is shareholder 1’s expectations of shareholder 2’s probability of tendering and V21(p) is shareholder 2’s expectations of shareholder 1’s probability of tendering, when 1 and 2 are playing tendering strategy. The expected utility of tendering for shareholders 1 and 2 are E(UT1) and E(UT2) respectively, and equal to the tender offer price. Similarly, the expected utility of not tendering is given by E(UN1) = V12(p) {1/2 [PL VL + (1-PL) VH G]} and E(UN2) = V21(p). {1/2 [PL VL + (1-PL) VH-G]}, respectively. Let (V1(p), V2(p)) is a pair of any other strategies and (V01(p), V02(p)), is a pair of equilibrium strategies for the shareholders 1 and 2. Equilibrium is defined as (V01, V02, V12, V21), s.t. U1(V01 (p), V12(p)) t U1 (V1(p), V12(p)  V1(p)

(3)

U2 (V02 (p), V21(p)) t U2 (V2(p), V21(p))  V2(p)

(4)

V01(p) = V21(p)

(5)

V02(p) = V12(p)

(6)

and expectations are realised in the equilibrium. If shareholders are following the pure strategy: 1 if p • V12(p) A V1(p) = (7) 0 if p < V12(p) A Similarly, 1 if p • V21(p) A V2(p) =

(8) 0 if p < V21(p) A

Where A is defined as A = 1/2 [PL VL + (1-PL) VH - G]. The probability of tendering Vk(p)[1, 0], if the shareholders are indifferent between tendering (T) and not tendering (N) their shares, i.e. E(UTk) = E(UNk).

Chapter 3

46

Consider a strategy vector in which both shareholders act optimally, and V12(p) = V21(p) = 1 V10(p) = V21(p) = [V01(p)=V02(p)=1]

(9)

V02(p) = V12(p) the price offered by the raider is p t A. Each shareholder has rational expectations about the other’s behaviour and in the pure strategy symmetric equilibrium both the shareholders tender their shares with probability 1. Here I define “symmetric” as a situation where the shareholders holding the same number of shares ought to behave identically. This implies that any other strategies are also the equilibrium strategy, i.e. (V01(p), V02(p)) = (V1(p), V2(p)). On the other hand, there is another pure strategy symmetric equilibrium, if p = 0 and shareholders tender their shares with probability V(p) = 0. From now onwards, I will not use double subscripts since I have shown by equations (5) and (6) that there exists a standard Bayesian Nash or Sequential Equilibrium. Proposition 1: Payoffs of the raider 3(T, p, V) and randomised payoffs for ith shareholder p, when others tender their share are given as follows: 3(T, p, V) =

§k · k (1- V ( p))k i ªi (V -G ) ip+G º -C V ( p ) ¦ ¨ ¸ « k » i=T © i ¹ k

¬

¼

And

(10a)

p=

+ )-G ª( § k  1· (k 1) (1V ( p))(k 1i) « V L P L V H P H ¸ V ( p) T © i ¹ k

k 1

¦¨ i

¬

)º » ¼

The Theory of Corporate Takeover Bids

47

As stated earlier, to simplify the matter, I consider a simple case of two shareholders (i.e. k=2) and one raider, and can work out the profits as follows: 0

if p=0

3(T, p, V)= V2(p)(V-2p)+2V(p)(1-V(p))[(V-G)/2-p + G]-C,

(10b)

if 0 < p < A V-2p-C

if p t A

The raider’s profits are given by 3(T, p, V) = (V - 2p - C), if there is a pure strategy symmetric equilibrium. Since both the shareholders sell their shares with certainty, the raider will make a bid as low as possible, i.e. p = A. The raider will buy from both and the raid will be successful. It is a necessary condition that a profit-maximising raider makes positive profits, i.e. (V-2p-C)>0. Proposition 2: Focusing only on symmetric equilibriums, if p=0 or p = A then there is only pure strategy equilibrium. On this basis, Grossman and Hart (1980a) assert that if the raider is more efficient than the incumbent management, makes a tender offer p t A and is restricted to an unconditional bid, then, in the pure strategy symmetric equilibrium, each shareholder tenders his share. The raider makes positive profits and dilution is necessary for a takeover bid to be successful. However, they completely ruled out the possibilities of takeovers by the inefficient raider. Proposition 3: If p=A, there exist pooling equilibriums in the pure strategy and the shareholders cannot distinguish whether the raider is efficient or inefficient. Grossman and Hart’s theory has some shortcomings. Their theory implies that either all shareholders will decide to tender their shares or all shareholders will refuse to tender in response to a tender offer by the raider. This kind of mechanism of takeovers does not seem to be consistent with the actual takeovers in the real world. The empirical evidence suggests that many takeover bids are completed without attracting tenders from all shareholders. There are basically two reasons for the common presence of

Chapter 3

48

unacquired shares in takeovers. First, even in a successful takeover bid, although the raider attracts the majority shares to gain control of the corporation, he does not usually attract tenders from all shareholders. 14 The empirical evidence supports a substantial and widespread incidence of such non-tendering. Frequently, as much as twenty to thirty percent of shareholders fail to tender their shares in response to an offer. 15 Second, in many takeovers, the acquirer does not buy all of the tendered shares. In “partial” bids, a frequently used device, the raider does not commit himself to purchase more than a specified fraction of the corporation’s shares. However, I will consider the improbable case of all shareholders tendering their shares because of the fact that when a tender offer is made shareholders randomise their payoffs. Consequently, the raider’s expected tender price will not be based on the extreme possibilities of tendering or not tendering by all shareholders but, rather, on the expected number of tendered shares. There often exist mixed strategy symmetric equilibriums, and they are easy to work out, since each shareholder has one share. That is, if shareholder 2 sells with probability V21(p), then shareholder 1 will also randomise if p = V12(p) A. For any tender offer p, such that 0 < p < A, at V12(p) = 0, V12(p) A is strictly smaller than p and V12(p) A at V12(p) = 1 is strictly greater than p. Since V12(p) A is continuous and strictly increasing in V12(p), there is a unique V12(p)  [1, 0] satisfying p = V12(p) A. Therefore, an equilibrium has shareholder 2 choosing a mixed strategy where V12(p) satisfies the equation p = V12(p) A. It is quite intuitive that pure strategy asymmetric equilibriums do not exist since the shareholders being situated identically cannot have asymmetric beliefs. To show that the raider earns strictly positive profits in mixed strategy symmetric equilibrium, I consider a scenario where shareholders have the same beliefs. Let p = V12(p) A, for any 0 < p < A 1 > V21(p) > V12(p) V01(p)  [1,0] => V12(p) = 0, V21(p)  [1,0] V02(p) = 0 and, if p = V21(p)A, for any 0 < p < A 1 > V21(p) > V12(p)

(11)

The Theory of Corporate Takeover Bids

V02(p)  [1, 0] => V21(p) = 1, V12(p)[1, 0]

49

(12)

V01(p) = 1 Equations (11) and (12), imply that 1 > ó12(p) = ó21(p). Hence, in equilibrium I have the following: V01(p) = V02(p)  [0, 1] => V12(p) = p/A = V02(p) = V01(p) = V21(p)

(13)

Proposition 4: Pair of strategies (V01(p) = p/A, V02(p) = p/A) is equilibrium if p  (0, A). Shareholders cannot distinguish between the types of raiders. Hence, there exist pooling equilibriums in the mixed strategy. That is, the probability of tendering lies between [1,0] and both shareholders tender in the mixed strategy symmetric equilibrium. To see that this equilibrium exists, I consider the raider’s expected profits, which are given as follows: 3(p, T, V) = V2(p). (V-2p) + 2.V(p). (1-V (p)){(V-G)/2 – p + G} - C

(14)

In the above expression, the first term of the right-hand side gives the raider’s expected profits when both the shareholders tender, and the second term give the raider’s expected profits when one shareholder tenders and the other shareholder does not tender. I substitute V(p) = p/A in the above expression, and on simplification, I get the following: 3(p, T, V) = p.(V/A) + p.(G/A) - p2. (G/A2) – 2(p2/A)- C

(15)

Since the raider chooses p to maximise his profits given V(p), this induces the sub-game. The optimal p maximises profits subject to the constraint p = V(p).A. There is a one-to-one mapping from p ->V(p). Hence, the two ways of looking at the problem are similar. So, I can analyse the raider’s choice of V(p) to maximise this expression. The first order condition gives us: p = (V +G)A/[2(G+2A)], and V(p) = (V+G)/[2(G+2A)] < 1. Proposition 5: The raider makes a tender offer p = (V+G)A/[2(G+2A)] and the shareholders tender their shares in a mixed strategy symmetric equilibrium with a probability of tendering V(p) = (V+G)/[2(G+2A)] < 1. The raider makes a

50

Chapter 3

conditional tender offer for any G  [0,f) and the raid is successful with positive probability. I assume that both the raider and the shareholders have rational expectations. Hence, I have to incorporate the rational expectations character into the Nash Equilibrium. This would mean, whatever may be the realisation of the value of corporation VL or VH, the shareholders will receive a signal through tender offer price about the exact value of corporation because of one-to-one mapping between p and V. For example, if V = VL, then PL = 1, and PH = 0. On the other hand, if V = VH, then PL = 0, and PH = 1. Such an assumption gives us a model parallel to Grossman and Hart’s, where they assume that both the raider and the shareholders know the potential value of the corporation. I examine whether dilution is necessary under these conditions as advocated for a successful takeover. Proposition 6: Shareholders know the true value of V, through a price signal. So either PL = 1 or PH = 1. Let us assume that the realisation of the corporation’s value is VL i.e. V=VL; then PL=1, and PH=0. On simplification, I get: A = 1/2 [PL VL + (1-PL)VH - G] = 1/2 (VL-G), and p = (V2L-G2)/(4VL), and V(p) = (VL+G)/(2VL) < 1 It is quite obvious that if G = 0, then p = VL/4. The raider makes positive profits if, and only if, G > C. Hence, we state a proposition: Proposition 7: If the raider is restricted to a conditional takeover bid for all shares of the corporation (unanimity), no matter whether the raider is efficient or inefficient, a Symmetric equilibrium exists at a price p = A and all shareholders sell their shares to the raider with probability 1. The raider makes positive profits if G > C. 16 Hence, there exist separating equilibriums in the subgame. For probability of tendering V(p) to be > 0 and less than 1, I get the following condition: VL > G => A > 0. Therefore, the dilution cannot be 100% and I state another proposition: Proposition 8: Mixed strategy symmetric equilibrium exists if dilution is not infinity (100%). Hence, there exist limiting equilibriums and not the equilibrium in the limit.

The Theory of Corporate Takeover Bids

51

I conjecture that the dilution may be unnecessary. Let G = 0 and analyse the equilibrium. Simplification will give p = [VL/4], and V(p ) = [VL/4A]0 in the pure strategy symmetric equilibrium. The raider’s profits in the mixed strategy symmetric equilibrium are positive if the expression VL2/8A-(VL - 2A) > 0. On simplification, I get 2A(VL/4A - 1)2 > 0. Since this expression is a perfect square, it will always be non-negative. I state another proposition: Proposition 9: The raider makes a tender offer p = VL/4 and the shareholders tender their shares with probability V(p) = VL/4A. The raid is successful with positive probability and the raider makes positive expected profits. Dilution is unnecessary in the mixed strategy symmetric equilibrium. The tender offer made by the raider may not be completely revealing if both the value of the corporation V and the cost of raid C are stochastic. 17 In that case, the shareholders will not be in a position to guess the correct value of the corporation through tender price, which may be low due to high cost or low value of the corporation. Hence, I cannot say V = VL with probability PL = 1.

3.4 Ex-Ante Efficiency and the Optimal Choice of Dilution This section will analyse the Pareto optimal choice of the dilution factor G. Holmstrom and Myerson (1983) distinguish between ex-ante and ex-post efficiency in order to evaluate the welfare consequences of the firm’s behaviour. Ex-ante efficiency measures welfare “before” the actual type of the raider; namely, efficient or inefficient, is known. It considers the expected outcome, given the uncertainty shareholders face in a takeover bid. By contrast, ex-post efficiency is the relevant concept for an uninformed social planner who is involved in formulating general policy rules that must apply to ex-post situations. When a social planner can tailor the policy to the actual situation, the concept of ex-post efficiency is applicable. Grossman and Hart do not make any distinction of this sort. Hence, our notion of welfare is quite different from that of Grossman and Hart. Given that all

Chapter 3

52

agents are risk-neutral and have the same utility function, the Pareto optimal choice of dilution G is that which maximises the sum of expected payoffs of the shareholders and the raider. I denote society’s return by R(G) and given by: R(GG) = [(VL+G)A/(G+2A)]+[(VL+G)2/4(G+2A)]-C

(17)

R(G) = r(G) + 3(p,T,V) When there is a raid, the efficiency gain is the increase in the expected profit of the firm minus the cost of resources used up in the raid. From equation (17) it is clear that the social returns R(G) equal the private return r(G) if the raider makes zero expected profits. But in that case, no raid will ever take place, since the raider incurs a positive cost. Hence, (v, c) is not realised. I consider the effect of dilution G on the returns to society R(G). The partial derivative of R(G) with respect to G gives us R’(G)>0 as long as G 0. From this assumption, each home or real property is worth 0 and V/n to the homeowners under the current and developer’s ownership, respectively. Let V be the potential value of the urban property under the developer’s ownership that V is bounded above and below (0 < V < 1). The developer spends C to find V, i.e. the cost of the search for the specific project. Let Q be the status quo or current value of the combined property of n residents (w.l.o.g. Q = 0). The number of risk-neutral homeowners or property owners is n and assumes that each owner holding one house or same

Modelling Real Estate Takeovers

65

proportion of property. Let T be the maximum dilution (an eminent domain) possible by the developer (through the government) in case there is any hold-out problems, if the developer is successful. 22 Deman (1991, 1994) defines ȍ ß, P) as the probability space, where ȍ is the sample space, ß is ı-algebra over a probability measure, and P is the probability. I define ĭ ȍ o R2, and the realisation of (v, c) = ijȦ  Assume that V and C are random variables with known distribution. The developer knows V precisely through a search cost. The price offered by the developer p is a function of (V, C) and is defined as: p: R2 o R+. The developer’s strategy is given by IJdijȦ  Each homeowner’s strategy is given by IJn(p) which is defined as follows: IJn(p): R+ o [S, NS], where S and NS stand for sell and not sell, respectively. The argument is the price offered by the developer IJdijȦ  Hence, the pure strategy of the homeowners is given by IJn: R+ o [1, 0] which is to sell or not sell in response to a price offer made by the developer. I define mixed strategies of the homeowners as IJMn: R+ x [S, NS] and is given by IJMn(p).

4.6 The Equilibrium Strategies and Outcomes of Takeover Bids Following Milgrom and Roberts (1982), and assuming that “nature” moves first and selects V from the range of urban property values V = {VL, VH}, according to the probability distribution Hi, given the homeowner’s subjective beliefs about the values of the urban property. Let V = {VL, VH} be the distribution that takes only two extreme values with positive probabilities. The informational structure of the game is that of symmetric, certain, complete but imperfect information. Consider a homogeneous case in which all the homeowners are identical. The homeowners are going to have the same beliefs about the value of the urban property. Let Į and (1- Į) be the probabilities that V is low and V is high, respectively. I consider this because, ex-ante, we are never sure whether or not a particular project will be efficient. Consider a simple two-stage game with three homeowners. Let one of them (to be called developer) observes ĭ and makes a sale offer of price p to the other two uninformed homeowners. In the game, I allow the developer to make only one offer. To gain control over the specific target area, the developer has to acquire both of the other homes. In the first stage of the game, the developer offers a price p based on his strategy IJdijȦ 

Chapter 4

66

Given the strategy of the developer, the second stage is the sub-game played by the homeowners, in which each homeowner has two possible actions: selling (S) or not selling (NS). Homeowners who are indifferent between selling and not selling in response to an offer will be assumed to sell. I take all players (the two homeowners and the developer) to be risk-neutral. Hence, the expected payoff or utility to homeowner 1 is the sum of expected values of his home if he sells and if he does not sell. I assume, for simplicity, if the takeover bid is unsuccessful, each home is worth zero (i.e., Q=0). Our results are not dependent on this assumption. The expected payoff of the homeowners 1 and 2 are given as follows: U1IJ1IJ12) = [ IJ1(p)p+(1-IJ1(p)) IJ12(p).1/2[PL VL + (1-PL)VH - T] 1: Yes 1:No, the Expected value of saying no when 1:Yes = Max ^SIJ12(p)A}

(1)

U2IJ2IJ21) = IJ2(p) p + (1-IJ2(p)) IJ21(p). 1/2[PL VL + (1-PL)VH - T] 2: Yes 2:No, the Expected value of saying no when 2:Yes = Max ^SIJ21(p)A}

(2)

Where IJ12(p) is homeowner 1’s expectations or conjecture of homeowner 2’s probability of selling andIJ21(p) is homeowner 2’s expectations or conjecture of homeowner 1’s probability of selling. The expected utility of selling for homeowners 1 and 2 are E(US1) and E(US2), respectively, and equal to the sale offer price. Similarly, the expected utility of not selling to 1 when 2 says yes and the expected value of not selling to 2 when 1 says yes are given by E(UNS1) = IJ12S ^>Į VL + (1-Į (VH – Ĭ)]} and E(UNS2) = IJ21S ^>Į VL + (1-Į (VH –Ĭ)]}, respectively. Let (IJ1(p), IJ2(p)) and (IJ01(p), IJ02(p)), be pairs of any other strategies and equilibrium strategies for the homeowners 1 and 2. Equilibrium is defined as (IJ01, IJ02, IJ12, IJ21) s.t. U1IJ01(p), IJ12(p)) • U1IJ1(p), IJ12(p))  IJ1(p)

(3)

U2IJ20(p), IJ21(p)) • U2IJ2(p), IJ21(p))  IJ2(p)

(4)

IJ01(p) = IJ21(p) and IJ20(p) = IJ12(p)

(5) & (6)

Modelling Real Estate Takeovers

67

and expectations are realised in the equilibrium. If homeowners are following the pure strategy: 1 if p • IJ12(p) A (7) IJ1(p) = 0 if p < IJ12(p) A Similarly, 1 if p • IJ21(p) A (8) IJ2(p) = 0 if p < IJ21(p) A Where A is defined as a convex combination or expected potential value and is given by A = >Į VL + (1-Į VH - Ĭ@ The homeowners’ strategies are given by probability of selling IJnS İ> 1], if the homeowners are indifferent between selling (S) and not selling (NS) their property or homes are characterised by: E(USN) = E(UNSN). Consider a Strategy Vector, in which both homeowners act optimally: IJ12(p) = IJ21(p) = 1 IJ10(p) = IJ21(p) => >IJ01(p) = IJ02(p) = 1]

(9)

IJ02(p) = IJ12(p) Where the price offered by the developer is p • A. Each homeowner has rational expectations about the other’s behaviour, and in the pure strategy symmetric equilibrium both the homeowners sell their homes with probability 1. By, “symmetric” I mean that the homeowners who are identically situated (i.e. hold the same number of homes) behave identically. This implies that any other strategy is also equal to an equilibrium strategy, i.e. (IJ1(p), IJ2(p)) = (IJ10(p), IJ20(p)). On the other hand, there is another pure strategy symmetric equilibrium: if

Chapter 4

68

S• and homeowners sell their homes with probability IJ(p)=0, the developer does not succeed. I rule out a possibility of asymmetric equilibriums and proof is trivial. Given the conditions for equilibrium, from now onwards I will use strategies and conjecture probabilities without double subscripts. Proposition 1: Profits of the developer 3(T, p, V) are given in pure and mixed strategies as follows:

0

3(T, p, V) =

If p=0

IJ2(p)(V-2p) + IJS -IJS ^9-Ĭ – SĬ`-C, (10) If, 00. Proposition 1 is more relevant to real estate than to stock market takeovers since profits to the bidder firm are consistently zero in the latter. Thus, while there is still an eminent domain issue in stock takeovers, prices are best characterised by competitive equilibrium. A generalisation of the developer’s profits is straightforward if there are n homeowners. Proposition 2: Focusing only on symmetric equilibriums, if p=0 or p= A then there is only pure strategy symmetric equilibrium. This is somewhat relevant to the stock market because of eminent domain holders of stocks who are forced to sell if the bidder succeeds in buying 50% of the stocks, i.e. (n+1)/2. The victims of eminent domains are the “optimists” and those who have specific capital in the stock, i.e. value the stock above the selling price. Optimists value their stock higher because their expectation about the value of the firm is high. On this basis, we can argue that if the developer is more efficient and makes a sell offer p t A and is restricted to a sell offer for any or all homes of the specific target area (i.e. an unconditional offer), then, in the pure strategy symmetric equilibrium, each homeowner sells his property. The developer makes positive profits, and the right of an eminent domain (i.e. dilution) is necessary for a takeover bid to be successful. However, this completely rules out the possibility of a takeover by an inefficient developer. Schall (1976) argues that, “if pre-renewal failure to internalise externalities produced the slum, the same behaviour may imply re-deterioration after renewal.”

Chapter 4

70

Proposition 3: If p = A, there exists pooling equilibriums and the homeowners cannot distinguish between the developers who are inefficient or efficient. In fact, empirical evidence shows that some takeovers do not work out well, and the developers turn out to be mistaken since ex-ante one cannot rule out the possibility of the takeover by a developer who turns out to be inefficient. In other words, the developer is successful, but the specific project that he undertakes may not be socially efficient and in fact he incurs losses. Myerson and Satterthwaite (1983), in a simple problem, suggest that there will be no way to ensure ex-post efficiency, but such a guarantee seems to be too much to ask for in this context anyway. I assume that both the developer and the homeowners have rational expectations and introduce rational expectations character into the Nash equilibrium. This assumption means that regardless of the realised value of the property (i.e. VL or VH), the homeowners get a signal from the price offered by the developer about the exact value of the property. This is because there is a one-to-one mapping between the offered price and the value of the property. Once the homeowners know, for example, if PL = 1, and (1- PL) = 0, then V = VL. On the other hand, if (1- PL) = 1, and PL = 0, then V = VH. That is to say, both the landowners and the developer have complete information about the potential value of the real estate property. I can examine whether an eminent domain is necessary in this case in the following proposition. Let the realisation of the property’s value is V=VL; by assumption that PL = 1, and (1- PL)= 0. On simplification, we get the following: A = 1/2[PL VL + (1-PL).VH - Ĭ@ = 1/2[(VL-Ĭ @ & p = 1/2[(VL-Ĭ  and IJS = 1 It is quite obvious that if Ĭ = 0, then 2p = VL/2 (i.e. one half of the potential value of the real estate or land). If the developer pays this price to the homeowners then he does not make any profits. Rather, he incurs a cost of going through the process of a takeover, and this cost is sunk as soon as the specific development project is abandoned. On the other hand, if Ĭ! the developer has an incentive to take over because he pays to the landowners less than the potential value of the property. The developer makes positive profits, if and only if, Ĭ > C. Hence, I state a proposition:

Modelling Real Estate Takeovers

71

Proposition 4: If the developer is restricted to a conditional takeover bid for all urban property (unanimity), a Symmetric equilibrium exists at a price p = A and all homeowners sell their homes to the developer with probability IJS = 1. The developer makes positive profits if Ĭ > C. 23 Unanimity means that the bid must be a 100% bid, i.e. for all the property or no deal, and the bidder gets to set the price; then the bidder has control over what he pays, and the chance of paying too much is nil. Every owner of the real estate has a reservation price and, therefore, there is some price at which 100% of the property will be acquired. But this price may not be one at which the developer can make money or a particular project undertaken by the developer to be efficient, hence we say he is inefficient. However, a widespread concern has been expressed in the literature on urban renewal and the use of the right of eminent domains, since it may in practice lead to dubious policies. It has been argued, at a theoretical level, that the holdout problem may not be a serious one. However, the holdout problem assumes serious dimensions when developers have inadequate bidding strategies, are inadequate bargainers, or when “a little lady who holds out forever” really does exist on a particular block of property. Unlike real estate properties, it seems likely that if bidding is done carefully and secretly most, if not all, houses on the block, can be bought up by a single developer before other owners find out. 24 This case is most likely if the absentee landlords own houses in the target area, having little or no contact with each other. Such a situation is quite consistent with the assumptions of the Grossman and Hart model for takeovers of the real estate properties. Hence, it is possible to realise pure strategy symmetric equilibriums. Now consider a situation where there are two pieces of land adjacent to each other. These two pieces of land are to be combined in order to build a shopping complex. A developer is interested in this specific project and would like to acquire these two pieces of land. As previously discussed, there is a possibility of taking over from the owners of the land by a unanimity rule, i.e. a unique best response (optimal constitution) will just as likely entail unanimity for all parties selling. However, there is a possibility that one of these two owners decides not to sell his land. Under these circumstances, a credible threat to exercise an eminent domain by the developer will persuade all parties to agree to sell. I am not arguing that ex-ante such a strategy is going to be socially efficient. However, this approach overcomes the boundary problem. The socially desirable symmetric equilibrium will crucially depend on the assumptions of

72

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complete indivisibility of redevelopment projects and atomistic property ownership. This will happen only if the project demands a zoning change, is of high commercial value, and the incumbent owners are basically homogeneous. However, many urban renewal projects do not match these standards. An inner-city residential redevelopment usually takes place in existing deteriorated neighbourhoods and thus does not require a specific scale, so long as it meets a threshold level. Hence, it would not be required of a developer to make a conditional bid in which he has to take over the entire block or abandon the project. Such a scenario can be explained by looking at the mixed strategy equilibriums. The concept of mixed strategy equilibrium is a limit of equilibriums, where each player’s payoffs are randomly perturbed by a small amount, unobservable to his opponent. Consider the improbable case of all homeowners or landowners selling their property because of the fact that when an offer of sale is made homeowners randomise their payoffs. The intuitive justification for a mixed strategy equilibrium is that, if the takeover bid makes the homeowners very nearly indifferent then, from the developer’s perspective, the actions of the homeowners would appear to be random. There often exist mixed strategy symmetric equilibriums, and they are easy to work out, since each homeowner has one home or piece of land. That is, if homeowner 2 sells with probability IJ21(p), then the homeowner 1 will also randomise if p = IJ 12(p) A. For any sale offer p such that 0 < p < A, at IJ 12(p) = 0, IJ 12(p)A is strictly smaller than p and IJ12(p)A at IJ12(p)= 1 is strictly greater than p. Since IJ12(p)A is continuous and strictly increasing in IJ12(p), there is a unique IJ12S İ> 0] satisfying p = IJ12(p)A. Therefore, an equilibrium has homeowner 2 choosing a mixed strategy where IJ 12(p) satisfies the equation p = IJ12(p)A. It is quite intuitive to show the absence of pure strategy asymmetric equilibriums, since players with identical information cannot have unequal beliefs. Proposition 5: Pair of strategies >IJ01(p) = p/A, IJ02(p) = p/A] is an equilibrium if p  (0, A). Homeowners cannot distinguish between the types of developers. Hence, there exist pooling equilibriums. Proof: We consider the following case where homeowners have equal beliefs: Let p = IJ12(p) A, for any 0 < p < A

Modelling Real Estate Takeovers

73

1 !IJ21(p) !IJ12(p) IJ10(p)  [1,0]=> IJ12(p) = 0 (11) IJ20(p) = 0

IJ21(p)  [1,0]

And, if p IJ21(p)A, for any 0 < p < A

(12)

1 !IJ21(p) !IJ12(p) IJ01(p)  [1,0] !IJ21(p) = 1 IJ02(p) = 1

IJ12(p)  [1,0]

Equations (11) and (12), imply that 1 > IJ12(p) = IJ equilibrium we have the following:

21(p).

Hence, in

IJ01(p ) = IJ02(p)  [0,1]=> IJ12(p) = p/A = IJ20(p) = IJ10(p )= IJ12(p) QED (13) That is, the probability of selling lies between [0,1] and both homeowners sell in the mixed strategy symmetric equilibrium. To see that this equilibrium exists, what I need to show is that the developer earns strictly positive profits in mixed strategy symmetric equilibrium. Consider the developer’s expected profits, which are given as follows:1 3(p, T, V) = IJ2(p).(V-S IJS -IJS ^9-Ĭ -SĬ`- C

(14)

In the above expression, the first term on the right-hand side gives the developer’s expected profits when both the homeowners sell (i.e. T=2), and the second term gives the developer’s expected profits when one homeowner sells and the other does not. We state another proposition: Proposition 6: The developer makes a sale offer p = 9Ĭ A/2Ĭ$ and the homeowners sell their shares in a mixed strategy symmetric equilibrium with a probability of selling IJ(p) = 9Ĭ)/2(Ĭ$ < 1. The developer makes a conditional sale offer for any Ĭ İ [0,1) and the takeover is successful with positive probability. Proof: From IJ (p)= p/A, we substitute in the equation (13), and on simplifications we get the following: 3(p, T, V) = p.V/A + p. Ĭ$ - p2 Ĭ$2 - 2p2/A – C

(15)

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Since the developer chooses p to maximise his profits given IJ(p) it induces in the subgame, the optimal p maximises profits subject to the constraint p = IJ(p) A. One can analyse the developer’s choice of IJ(p) to maximise this expression. The first order condition gives: :p = >9Ĭ $@>Ĭ$ @DQG IJ(p) = >9Ĭ @>Ĭ$ @ < 1. Q.E.D I state another proposition. Proposition 7: Mixed strategy symmetric equilibriums exist if eminent domain is not infinity (100%). There exist limiting equilibriums and not the equilibriums in the limit Once again, assume that both the developer and the homeowners have rational expectations and incorporate the rational expectations character into the Nash Equilibrium. Such an assumption gives us real estate takeover model parallel to Grossman and Hart’s model for corporate takeovers, where they assume that both the raider and the shareholders know the potential value of the corporation. I will examine whether dilution or eminent domain is necessary under these conditions as advocated by Grossman and Hart for a takeover mechanism to be successful. I assume that the realisation of the real estate property’s value is VL, i.e. V = VL; by assumption of ȇL = 1, and 1-ȇL = 0. On simplification: A = ½ >ȇL VL + (1-ȇL)VH - Ĭ@ = ½ (VL-Ĭ  and we get: p = (V2L -Ĭ2)/4VL, and (p) = (VLĬ 9L < 1 For the probability of selling IJ(p) to be positive and less than 1, we get the following condition: VL > Ĭ => A > 0. Therefore, I conclude that the eminent domain cannot be infinity (100%). Q.E.D. I state another proposition: Proposition 8: The developer makes a sale offer p = VL/4 and the homeowners sell their property with probability IJ(p) = VL/4A. The takeover is successful with positive probability and the developer makes positive expected profits. The dilution is unnecessary in the mixed strategy symmetric equilibrium. Proof of Existence: I conjecture that the eminent domain may be unnecessary. On substituting Ĭ = 0, I get p = V/4, and IJ (p) = VL/4A < 1. 25

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In this case, the developer’s expected profits are given by: 3(p, V, T) = P.VL/A - 2p2/A - C = V2L/8A – C

(16)

To see whether the developer makes positive profits or not, we look at the condition for a profit-maximising developer (VL - 2A - C) > 0 in the pure strategy symmetric equilibrium. The developer’s profits in the mixed strategy symmetric equilibrium are positive if V2L/8A-(VL - 2A) > 0. On simplification, we get 2A(VL/4A - 1)2 > 0. Since this expression is a perfect square, this expression will always be non-negative. Hence, the developer makes positive profits. Q.E.D. The sale offer made by the developer may not be completely revealing if both the value of real estate property V and the cost of raid C are stochastic. 26 In that case, the homeowners will not be in a position to guess the correct value of the real estate property through the sale price, which may be low due to the high cost of the takeover or low value of the real estate property. Hence, we cannot say V = VL with probability Į = 1. The existence of the mixed strategy equilibriums without the dilution shows that we do not really need assumption of the continuum of owners, since there is no residual problem of the disappearance of information in a finite players’ game. In fact, when considering the problem of the developer negotiating with homeowners, a model of finitely many owners appears to be much more realistic. It is well known that takeovers do occur with positive probabilities in models with finitely many players. This result holds independently whether or not these finitely many owners believe that they have an impact on the success of the sale, as pointed out by Shleifer and Vishny (1986), Bagnoli and Lipman (1988), Deman (1991, 94), etc.

4.7 Ex-Ante Efficiency and Optimal Choice of Eminent Domain A broad range of policy questions and opinions have evolved relating to the economic consequences of urban renewal through a takeovers mechanism. For some economists, like Grossman and Hart, the takeover mechanism creates real market value for both the developer and homeowners of the specific target area (i.e. the outcomes are Pareto superior). Therefore, takeover bids should be encouraged. However, there is a well-known traditional “holdout problem” in the literature on neighbourhood externalities, where the last seller of the old structure holds out for a tremendously high price. If the developer has to pay all his potential profits from the redevelopment to the last seller, this discourages potential

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developers from making property takeover attempts. Under such circumstances, we end up with a block of decaying houses, a status quo representing an inefficient Nash outcome or slum equilibrium. It is argued from a social standpoint that permissible dilution residents forced to sell (through intervention) should be at least large enough to increase the probability of a successful takeover of the urban property increases. Furthermore, in the presence of a large threat of dilution, the status quo market value of the urban property will be higher, since the residents will be induced to make property improvements on their own, which, in turn, will increase the bidding price for the developer. Hence, the takeover of the urban property will be difficult because the developer has to offer a high price if he wants to be successful. This view appears to be consistent with information-based explanation of takeovers. At the other end of the spectrum is the view which clearly opposes any kind of intervention. It has been suggested that the cost of reduced redevelopment may well be less than the cost of misused applications of eminent domain in urban renewal. What has not been discussed and analysed is the appropriate limit on dilution if such provisions are made. Below, we consider the Pareto optimal choice of the eminent domain Ĭ Rothenberg (1967) justifies urban renewal efforts in Chicago, and there are a few other examples in the literature of urban renewal where such projects were socially justified ex-post. Holmstrom and Myerson (1983) distinguish between ex-ante and ex-post efficiency in order to evaluate the welfare consequences of the firm’s behaviour and we use the same concept for real estate property. Ex-ante efficiency measures welfare “before” the actual type of the developer, efficient or inefficient, is known and whether or not the takeover will be successful. Ex-ante efficiency considers the expected outcome, given the uncertainty homeowners face as the relevant concept for an uninformed social planner who is involved in formulating general policy rules. When a social planner can tailor the policy to the realised outcome, the concept of ex-post efficiency is applicable. No such distinction has been made in the urban redevelopment literature. Therefore, our notion of welfare differs from the existing debate on the issues in question. Given that all agents are risk-neutral and have the same utility function, the Pareto optimal choice of eminent domain Ĭ is that which maximises the sum of expected payoffs of the homeowners and the developer. We are assuming that there is no distributional effect, i.e. transfer of wealth from homeowners to the developer or vice-versa. Hence, we are looking at a Pareto improvement case rather than a rent-seeking problem. We denote society’s return by

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5Ĭ  which is given by: 5Ĭ = [(VL + Ĭ $@Ĭ + 2A) + [(VL + Ĭ @2>Ĭ + 2A)] – C (17) 5Ĭ = UĬ + ʌS79

(18)

In equation (17) the first term on the right-hand side is the expected gain to the homeowners and the second term is the expected gain to the developer. When the takeover is successful, the efficiency gain is the increase in the expected value of the property minus the cost of resources used up in the takeover process. From equation (18) it is clear that the social returns 5Ĭ equal the private return UĬ if the developer makes zero expected profits. But in that case, no developer will ever make any attempt to take over, since the developer incurs a positive cost. Hence (v, c) is not realised, and homeowners remain in slum equilibrium. Consider the effect of dilution Ĭ on the returns to society 5Ĭ  The probability of tendering IJ(p) increases with Ĭ The partial derivative of 5Ĭ with respect to Ĭ gives us 5¶Ĭ ! as long as Ĭ < V. This implies that there does not exist any optimal value of dilution Ĭ for society in the mixed strategy symmetric equilibrium. This is quite intuitive because a large dilution implies that (V-Ĭ 1 will decrease, i.e. an increase in surplus (p-(V-Ĭ 1 would work in favour of the developer. Specifically, the larger the difference between the expected post-sell market value to non-selling landowners and the status quo market value of the real estate, the larger the opportunity cost of not selling if the developer is successful. Hence, this process is coercive and induces landowners to sell. In the limit, the homeowners might receive nothing if the dilution is 100% (i.e. given Ĭ İ [0, V], if Ĭ = V, then p = 0 and in that case IJ (p) = 1 and takeover of the specific project must be successful. However, in that case, mixed strategy equilibrium does not exist. Hence, I state a proposition: Proposition 9: 5Ĭ is strictly increasing in Ĭ for values of Ĭ < V. If dilution Ĭ -> V, mixed strategy equilibrium does not exist in the limit. On the other hand, the partial derivative of the expected utility function of the landowners with respect to Ĭ gives us 8¶Ĭ < 0, which implies that the landowners would like to keep Ĭ as small as possible, i.e. Ĭ  if there are no transfers of wealth. Hence, the homeowners’ interests and societal interests conflict with regards to the appropriate level of dilution. However, the society is better off by keeping dilution as large as possible but less than infinity.

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4.8 Conclusion and Direction for Future Research Bagnoli and Lipman (1988), Hirshleifer and Titman (1990), Deman 1991, 94) have argued that the Grossman and Hart characterisation of the real world of pure strategy equilibriums seems to be somewhat unrealistic. Hence, the extreme cases of pure strategy equilibriums are more likely to be found in real estate takeovers than in the market for corporate control. The assumption of either impotent managers or complete absence of management is also more consistent with the real estate market than the market for corporate control. We have developed a game-theoretic model of urban property takeovers and have shown that there exists a pure strategy symmetric equilibrium. It is possible to realise this pure strategy symmetric equilibrium. A coherent approach to interference by way of exercising the right of eminent domain has been discussed. The possibility of taking over urban property or plots of land by an inefficient developer in the name of either urban renewal or site assembly is not completely ruled out. Hence, the applications of eminent domain, such as urban renewal, are often either (i) socially inefficient, but beneficial to selected individuals or groups at the expense of others; or (ii) socially inefficient because the owners are truly harmed by the use of eminent domain if their dwelling and surrounding neighbourhood are really worth to them more than the “just compensation” allowed by the courts. The main conclusion of the paper is that the threat of takeover can facilitate a redevelopment programme undertaken by a developer even though the equilibriums are straightforward in a finitely many players’ game, for the reasons stated above. I also show that the developer faces a trade-off between a low bid price and a high probability of the takeover. However, the probability of takeover can be enhanced by the provision of dilution or exercise of right to eminent domain. This paper makes a useful application of game theory and corporate finance to address policy issues of dilution, imminent domain, slum equilibriums, and other urban renewal problems. The paper also provides evidence in favour of how the market for development purchases should be organised. In fact, it seems like a potentially interesting idea and it might even be possible for a local government to adopt such a rule. To minimise government abuse of the right of eminent domain, and to enhance the effectiveness of using eminent domain as a threat by the developer, I introduce a democratic (50% yes vote) or super majority rule in the model (to pass a constitutional test). The results here are significantly different from those already published and will appeal to a wider audience from finance, industrial organisation, game

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theory and urban economics. The paper contributes to the ongoing debate on the subject of takeovers. I believe the limiting case of the finite owner model, as the number of owners tends to infinity, differs from the continuum case. However, it can be shown that a finitely many players’ model with a noise will give the same results as the continuum of players’ model. A generalisation of such a model is not difficult, but preliminary results may be useful in formulating public policies regarding privatisation of urban renewal efforts.

CHAPTER 5 TAKEOVERS AND MERGER OF BUILDING SOCIETIES

5.1 Introductions and Historical Background Building societies came into existence during the second half of the eighteenth century in response to prevailing economic and social needs, growing sophistication of financial institutions and the industrial revolution. The first known building society was established in Birmingham in 1775 and it is estimated that by the end of the century between twenty and fifty had been established, predominately in the Midlands, Yorkshire and Lancashire. The number of societies began to decline, however, in the late nineteenth century and today there remains only 84 building societies, for example, Table 1 & Figure 6 provides an historical account of decline in numbers of societies over the years. Table – 1 Years

No. of Soc.

Years

No. of Soc.

1900

2286

1960

726

1910

1723

1970

481

1920

1271

1980

382

1930

1026

1990

84

1940

952

2000

65

1950

819

2008

59

Source: Gough (1995), The Economics of Building Societies Updated

There are a number of ways in which building societies can merge. However, two main forms are prevalent: societies can either merge through

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the amalgamation of two or more societies or through transfers of engagements from one society to another. An amalgamation can be seen as a coming together of two societies, the new society often having a name derived from its two predecessors. A transfer of engagements is, essentially, a takeover, in which the smaller society loses its identity and its independence. Of the 796 societies on the register at the beginning of 1953, over half had transferred their engagements to other societies by the end of 1980. During the 1980s, the number of societies reduced to more than one half, again largely due to extensive intra-sectoral takeover activity, and the number reduced to 59 by 2008. Mergers usually took place among neighbouring societies, thus transforming local societies into regional societies or strengthening the regional base of those few societies that were already becoming nationwide organisations.

Merger of Building Socities

No. of Socities

2500 2000 1500 1000 500 0 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 Years

Figure 6

Geographical extension of societies beyond their own head offices, through an extensive branching policy, has been a major influence on growth and amalgamation in this sector. Building societies may see a move into a new geographical area as being simplified via a process of transfers of engagements from smaller to larger societies. The decrease in the number of societies, either by termination or amalgamation, has been largely compensated for by an increase in the number of branches. Recently, most of the decline has been in the smaller asset volume, local societies, although a number of middle to upper range regional societies

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have also disappeared. The regional nature of this decline, mostly from the impact of the recession on the housing market, has meant the South of England experiencing a much more dramatic fall in society numbers than elsewhere. A main feature of this decline has been the high proportion ‘encouraged’ by The Building Societies Commission (BSC) as a consequence of building societies finding themselves in financial difficulties. An increased concentration may be inevitable if the recent housing downturn is sustained. The Building Society Commission may have to further intervene in the future to ‘rescue’ more societies, which find themselves in troubled waters. Mostly the Building Society Commission has intervened after the violation or near violation by societies of minimum capital requirements. Depending on the gravity of the situation, it has either ordered or actively encouraged the offending society to seek a rescue through a transfer of engagements to another society. Given the asset size of some of these societies, only the larger national societies have had the resources to absorb poorly performing societies without adversely affecting their own financial position. There is no reluctance among the national societies to rescue troubled counterparts, as often they can take control at a low cost. Today, few new societies are brave enough to establish themselves. Any new society has to compete with 10–15 large societies operating in its area. Existing small societies are being absorbed, whilst the birth rate of new societies continues to be extremely low. Several notable exceptions to this rule do exist, however. Irish-based societies have been establishing in Northern Ireland and elsewhere in Great Britain, and centralised mortgage lenders have been setting up new business as another player in the mortgage market. From the statistics, we have seen how a large number of small building societies have been transformed into a smaller number of larger building societies. It may seem sensible to conclude that this would not have happened if advantages to building societies from mergers and acquisitions, at least in partial equilibrium framework, did not exist. The objective of this section is to discuss the reasons for transfers of engagements and the benefits they bestow on the parties involved and affected. Lloyds Bank, the first real experience of an outside institution to move into the industry, will place a special emphasis on the takeover of the Cheltenham and Gloucester (G&C) Building Society. First, however, this section begins with exploring the motivation behind takeovers and mergers and an analysis of the welfare of the recent merger phenomenon on the varying sized societies.

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5.2 Motivations Behind Mergers of Building Societies A: Local and Spatial Context Small local societies, which have always provided a particular and useful service in their own areas may, if two are within the same area, consider merging. Local societies often find the many regulations surrounding their work difficult and could merge to decrease their cost of operation. They then form a strong viable society better able to survive and maintain services. A study by Davies, G. and M. Davies (1981) shows a more efficient branch network is often created as a result of merger, meaning the coverage of the same territory by a rationalised new single unit. In this process, mergers and branching are complementary activities. However, even when two such societies do merge this still might not create a viable new organisation. This might only be achieved through further mergers, at a much larger level of operations. Different reasons exist to explain the takeover of smaller societies by larger ones. Scale efficiency can often be a motivating factor, and a more efficient use of capital or lower average operating or funding costs could result on economies. Often, a larger building society by its geographical location might be attractive to a potential target. A national building society may attract a local society if it feels it has a deficiency in its branch network in that particular area, and it sees the addition of two or three branches as a remedy to this. Local societies, with their intimate knowledge of social and industrial conditions in their locality and of local people and their attitudes and traditions, are in a position to provide a specialised service to their own community. Larger societies, recognising this local advantage, may leave the local society to work as a wholly owned subsidiary post-acquisition, feeling it still has an important role to play. However, because many of the smaller societies have concentrated on a core business over the years, namely mortgages, a diversified product range is not usually a side effect of mergers. The corollary of this is that it has become more difficult for the smaller societies to survive, and an ability to develop niche markets has proved important as acquisitions are often seen as an efficient way to build up the size of a group. If a society does not have a viable future, it may be in the interests of members, and the building society movement in general, that a merger takes place. Mergers create new, larger scale financial institutions, which are better placed to protect their home market share. Also, the Building Society Commission may force the merger upon building

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societies. Any society which tries to expand too fast, either via acquisitions or otherwise, and makes a loss may be compelled to accept an offer from a larger society, due to intervention by the Building Society Commission. Special features of a local society may also make it an attractive prospect. For example, a head office in a booming part of the country, a larger amount of reserves, good cost to income, or capital adequacy figures may all induce takeovers. Regional societies also take over small societies. A regional building society may see this as an opportunity to consolidate in a certain area and to decrease the competition by removing one of the players from the arena. They may also feel that, by forming a larger group, they are decreasing the possibility of becoming a takeover target themselves. Some of the smallest building societies may avoid takeover altogether because their size, customer base or asset level does not justify the search and administration costs of a takeover. This works like a poison pill for corporations.

B: Merger of Societies in a National Context Towards the middle to late 1980s, a series of mergers occurred between national building societies. Notable examples are the mergers between the Alliance and the Leicester and the Nationwide and the Anglia. The rationale underlying these mergers was to create sufficient critical mass to allow the society to offer an enhanced range of financial services and to enable it to compete with the retail banks. Society size is an important factor in determining cost efficiency, which is, in turn, reflected in the society’s profit. Many of the reasons for the merger between a local and a national society also apply to a merger between two national societies. The realisation of benefits from economies of scale is an important rationale for increased concentration. The merger of two institutions encourages the establishment of extensive back-up services, for example, legal, computing and consultancy services. Additional capital strength also enables institutions to venture into markets outside their home country. Acquisitions are one of the primary mechanisms through which foreign markets can be accessed. This makes available an already established product portfolio, customer base, distribution network and expertise of the local market. Similarly, foreign institutions may see the takeover of a British building society as an ideal way to gain entry into the United Kingdom market.

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C: Impact of Takeover Waves in Other Sectors Mergers have contributed much towards the average size of societies. The merger movement also appears to have depressed the relative progress of those societies, which have not, during the period in question, been engaged in absorbing other societies. Whilst small societies are often involved in mergers, it should not be thought that this is always the case. The merger movement is a rather more general phenomenon. Nevertheless, almost all societies have found it possible to come to terms with recent changes in their markets without changing their essential identity. Only two, Abbey National and Halifax, have so far found the industry too restrictive and converted to a plc. Many large societies have, however, fostered links with other institutions. In particular, they have purchased or formed strategic alliances with insurance companies, to gain commission on the sale of endowment policies, and estate agents, to enhance their distributional capabilities. Building societies’ joint ventures and acquisition strategies originate from a desire to develop more quickly commercial know-how in new product areas than would be possible through a go-it-alone strategy. Joint ventures can provide a speedy channel acceptance, reduce market costs, increase sales volume, and provide for important production cost savings. Furthermore, as the importance of information technology increases, an important consideration in the viability of any proposed merger is the question of systems compatibility. This may even prove to be an important inducement, or barrier, to merger. Also, the management of a society has the responsibility to make their organisation grow. This is often achieved more effectively by acquiring an existing business rather than starting from scratch. As already stated, merging can eliminate duplication, improve efficiency, enhance a product range, speed up entry into new technology, and aid geographic expansion. It is also noteworthy, that on the retail deposit side, the Alliance & Leicester acquired Girobank. This allowed them to put the personal banking side of Girobank in the Alliance & Leicester, and amalgamate the personal business side of the two organisations. They believe that their customers now benefit from a banking experience and products delivered with the ‘friendliness’ of a building society. For example, Girobank’s expertise in telephone banking is now available to the building society account holders. This move by the Alliance & Leicester may turn out to be unique for the simple reason that small or medium-sized banks no longer exist. Gough (1979) argued that there was no evidence that larger societies are anyway more efficient than smaller ones. He attributed merger activity to

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managerial discretion by acquisitive managers. Barnes (1985) found further support for this conclusion. He tested the hypothesis that merger benefits arose in terms of improved management expenses ratios and increased growth rates. Management expenses are an accepted synonym for operational costs in the industry, as a society, which manages funds at a lower cost, may be considered more efficient. Management expenses of a building society are a function of the number and type of staff, size, location of offices, number of branches, etc. As mergers are often considered beneficial, a more viable society is expected. Operating costs and growth rates should improve. In terms of the former, Barnes (1985) does not find any support, either in the short or long-run. In fact, the evidence suggests a tendency towards higher operating unit costs, even though societies were merging in the hope of becoming, in terms of size, more economic units. The evidence on the latter in his study was deemed inconclusive, but the doubts he raises give enough scope to believe there exist other reasons for mergers that should be considered.

D: Motivations of Managerial Self-Interests Mergers may be advocated on the basis of the interests of directors, members, and staff. For directors, there is the chance to serve in a larger organisation with perhaps better conditions. Staff may have enhanced prospects of promotion, better training, higher salaries and pension benefits. For members, the benefit may come in participating in the resources built up over the years. This may involve a bonus paid following the merger or a higher rate of interest for a fixed period. As stated before, a heavy emphasis is often placed on growth as an objective, and the personal objectives of staff may also be best served by growth. Whilst growth can be achieved internally, it can also be achieved through mergers with other societies. For this to be the case, Gough (1979, 1985) argues that two conditions must be fulfilled: firstly, that the initiative to merge should come from the management of the society, and secondly, that the salary structure should be such that higher salaries are paid in larger organisations. In Gough’s opinion, both these conditions are normally fulfilled.

E: Motivations of Inter-Sectoral Interests In general, there are several reasons why an outside institution might want to enter the building society sector. Over the past few years, the building society sector has collectively outperformed the major United Kingdom clearing banks in practically all measurable performance areas, for

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example, see Markey (1994). The building society record in maintaining their net interest margin has been consistently better than the banks. Building societies generally enjoy much lower cost to income ratios, due to simpler product ranges, smaller branch networks, and superior technology. Despite having a less diversified lending portfolio, building societies have always experienced far less bad debt problems than the banks. Being less vulnerable to the bad debt cycle building societies can enjoy much more stable earnings flows than banks, which facilitates more efficient budgeting and planning. Therefore, an institution, such as a bank, may see a takeover of a building society as an easy way to gain these advantages. The C&G was a main target of the merger because it had the lowest of the low cost to income ratios in the sector. Also, the C&G’s policy was to have a simple and focused approach to their business. They did not aim for the high transaction customer. In fact, the C&G was the only large building society, which did not offer a chequebook facility. This clearly indicated that it did not duplicate Lloyds’ portfolio, and thus may well have been an important influence on the bank. Another possible explanation of such a move is to gain expertise in the mortgage market. In the 1970s, building societies dominated this market, but in the early 1980s, banks and other specialist mortgage lenders entered the market aggressively and captured a significant market share from the building societies. This was rather short-lived, and for the last few years building societies have again been dominating this market. Societies now have improved treasury departments, computer systems, and marketing departments to enable them to offer a multitude of innovative mortgage products targeted at various segments of the market. There is also a public awareness that building societies have, on the whole, been offering better mortgage deals throughout the period of the present housing recession. As was stated before, only a small proportion of Lloyds Bank customers use the bank for their mortgage. This means the bank, by diversifying into the mortgage market via a takeover, has a large customer base to target. An institution with excess reserves, which have been built up over the years, may see the takeover of a building society as a very appropriate way to use these—gaining entry into the sector without itself having to borrow money or issue further shares on the stock market. This was a primary reason for the Lloyds’ move. Over a few years, their reserves have been built up as in Table 2.

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Table – 2 Year 1989 1990 1991 1992 1993

Reserves Level (m) 1134 1222 1270 1460 1747

Source: Lloyds Bank Annual Report 1989–1993

Another worrying factor, which the banks have to address, is that the public generally prefers building societies to handle their mortgages and related financial products, for example, see Barnes (1985), Markey (1994), etc. This view has been highlighted during the recent recession, as banks received bad press about their treatment of small businesses and private investors. A bank could conceivably see the takeover of a building society as a way to circumvent this view, allowing the society to maintain the public facade, and hence the public’s goodwill.

5.3 Inter-Sectoral Takeover Mechanism In April 1994, the Board of the Cheltenham and Gloucester Building Society announced the transfer of its business to a limited company within the Lloyds Bank Group and became Cheltenham and Gloucester plc, a wholly-owned subsidiary. C&G ceased to be a building society and became an authorised institution under the Banking Act 1987. The Board of the Cheltenham and Gloucester informed its members that they had decided the best way forward, in order to develop business in the interest of customers and staff, was to join the Lloyds Bank Group. This decision was taken after conducting a wide-ranging review of investment and mortgage markets of the C&G in which they were competing. The move was the first takeover of a British building society by a bank. The takeover was completed after 75% of eligible investors voted, and a simple majority of the borrowers who voted gave their approval. 27 C&G would take on responsibility for all Lloyds Bank’s new United Kingdom residential mortgage business, and would continue to operate as before the merger, retaining its own identity, setting its own interest rates, and offering its own brand of savings and mortgage products to customers. It would not be tied to Lloyds’ products. Several commentators, for example, Markey (1994), Barnes (1985), and Gough (1982) felt, however, that C&G cannot maintain this ‘independent’ status in the group for long,

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believing Lloyds will eventually request them to market their products. The deal would mean that the two groups together would hold around 7% of the total United Kingdom home mortgage market, making them the fourth biggest lender after the Halifax, Abbey National, and Nationwide. The C&G was the sixth largest building society and had one million savers and 370,000 borrowers prior to the merger. It had the lowest cost to income ratio in the movement at around 26% compared with an average of about 48% of all societies, and over 60% at Lloyds. Both operations were deemed to be well-managed. Lloyds had acquired the reputation of being Britain’s best-managed bank as a result of its remorseless squeeze on costs. At the time of the offer, only 4% of Lloyds’ customers bought a mortgage through the Bank, offering a huge market to be tapped. Lloyds believed the combination of their ability to raise funds in the wholesale money markets at a cheaper rate than C&G, combined with C&G’s low cost of distribution, will have huge competitive advantages. For Lloyds, the deal represents an opportunity to make use of its capital strength to increase its grasp on the home market. This was all reflected in the share price movements of Lloyds and its main rivals of the day following the announcement of the takeover. The fact that Abbey National’s mortgage business stood to lose considerably from the takeover is reflected in Table 3. Table 3 Company Lloyds Bank Abbey National Barclays Bank NWB RBS HSBC FTSE 100

Daily Movement 44p up 19p down 8p down 4p down 5p down 23p down +2.9

Closing Price 581p 445p 508p 446p 396p 723p 3101.2

Percentage Change 7.6% 4.1% 1.5% 0.8% 1.2% 3.1% 0.1%

Source: The Times 22 April 1994

Lloyds was offering all C&G’s investors and borrowers a one-off bonus of up to £ 10000.00 to accept the takeover deal. Under the proposal, Lloyds agreed to pay a total of £ 1.8 billion. Some analysts viewed this offer as low, many feeling that the society was worth over £2.5 billion. Before the takeover bid, Lloyds was doing well but commentators were concerned about its next move. Lloyds Bank kept their cash mounting. It was 2.1 times

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book value and 14 times historic earnings; the acquisition was not expensive as banking deals go and will look even cheaper in a year when Lloyds is due to pay the £ 1.8 billion. It is believed, with this low-cost acquisition, Lloyds Bank could launch a price war in the mortgage and savings market and still deliver above-average returns to shareholders. Lloyds Bank plans to pay for the takeover out of its own resources and has no plans to raise extra funds from shareholders to complete the deal. The sum would have been distributed amongst the members and staff £500 for each voting investor plus 10% of the balance of their account. C&G encouraged their customers to keep their accounts open to ensure they benefited from the possible payment. Concern was widespread at the time, however, that the one-off payment by Lloyds would not allow account holders to reap the future profits of what is generally acknowledged to be one of Britain’s most promising financial services businesses. It should be noted that it was C&G which started the process, and out of a short list of potential buyers, Lloyds emerged as the favourite. The deal, however, also required various regulatory approvals, including a High Court judgment to clarify aspects of the 1986 Building Societies Act. This was where the main problem arose. The High Court ruled that the takeover under the proposed terms was illegal. Despite C&G’s claim that there was a loophole in the law and that payments could be made to members of less than two years standing, this was not the intention of Parliament. The 1986 Building Society Act states that only members who had held voting accounts for at least two years could receive any share of the £1.8 billion. On 11 August 1994, C&G announced a revised plan to distribute £1.8 billion. According to the new plan, the chances of the members of the society voting in favour of the proposed takeover had increased. Nearly 400,000 of C&G’s members lost on bonuses, but those who did qualify received as much as £13,500, the average pay-out being £ 2,000. Each member received £500 plus of their account balance. C&G also paid its staff members £500 each out of the society’s reserves.

5.4 Lloyds Bank v Cheltenham & Gloucester Performance If you analyse the performance record of C&G and Lloyds Bank, then it tells an altogether different story. For example, according to the Data Monitor C&G made an average of £82 profit, per customer, which has turned out to be one of the highest when compared with Halifax, Alliance & Leicester, Nationwide, Woolwich, Leeds Permanent, Bradford & Bingley, Britannia, Bristol & West, and Yorkshire. In a report, C & G had disclosed a

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44.5 % increase in first-half pre-tax profits from £75.3 million to £108.8 million. It has only 236 branches and mortgage centres, contributing to a low cost to income ratio of about 26% compared with the Halifax’s 40 % and an average of about 46% for all societies and 60% for Lloyds. In general, building societies are less vulnerable to bad debts cycles, and therefore enjoy much more stable earnings flows than banks. C & G, in particular, had experienced far less bad debt problems than Lloyds Bank even though it had a less diversified lending portfolio. Because of its aggressive approach to the mortgage market, its lending rose by 30% to 1.48 billion and loss provisions fell by 63% from 63.6 million to 23.5 million. Conversely, Lloyds Bank has been struggling to recover it’s roughly £1.6 billion bad debt. In fact, over the last few years, the building society sector has collectively outperformed the major UK banks in practically all-measurable areas of performance. Furthermore, building societies are known for maintaining their net interest margin consistently better than the banks. Further empirical studies do not seem to support the view that the growth rate and operating unit costs improve in the long run after the merger of societies. Barnes (1985) concluded in his empirical study that the tendency has been towards higher operating unit costs, and evidence on growth has been inconclusive. If the idea behind the merger is to realise the scale of economies ex-post, then Gough’s (1982) study does not find any support that large societies are in any way more efficient than the smaller ones. In fact, according to his study, they turned out to be size neutral. One can also evaluate the proposed corporate merger in the background of three additional motivations and explanations for acquisitions; namely, corporate raider, information-based, and market power. However, empirical evidence is inconsistent with the corporate raider and market power hypotheses, and there is little support in favour of either.

5.5 Inter-Sectoral Merger - Search for Theories Thompson (1997) nicely summarises nine competing theories discussed by Caves (1989) into five categories. However, there appear to be broadly two competing theories of the firm in the industrial organisation literature, which are often used in explaining merger motives. According to the neo-classical theory of profit maximisation, firms will go for the merger if the forces of competition can result in an increase in shareholders’ wealth. After the merger, besides the rationalisation of industry argument, it can also create monopoly power and increased operating efficiency. Unfortunately,

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the neo-classical paradigms do not seem to hold in explaining a number of phenomena in finance. Alternative theories of the firm due to Baumol (1959), Marris 1964), Williamson (1974), Leibenstein (1976) and others have argued that the objective of the firm is to maximise managerial utility. The managers go beyond the level of ‘satisfactory’ profits and attempt to maximise their own utility. This is where the conflict of interest begins—between the interests of the owners-depositors in mutuals and the managers. This takes the agency theory, prisoners’ dilemma situation, and us into the third approach. Building societies do have special characteristics, for example, their role as specialist intermediaries, an absence of the right to sell claims in a secondary market, the right to demutualise by paying compensation, the decision on one-member-one vote rule, guaranteed deposits, etc. The UK building societies and other financial mutuals do suffer from an acute agency problem. Using Grossman and Hart’s (1980a) argument, no individual owner-depositor will have a large enough incentive to devote his resources to ensure that the management acts in their best interests. Individuals have an option to free ride, secure in the knowledge that the regulatory process renders their deposits de facto risk-free investments. Even if dissatisfied members succeed by forming a coalition against the incumbent management, all other members will have a free ride on their activism. 28 It is clear from Chapter 2 that in corporations this free-rider problem can be overcome by the use of the takeover mechanism, the main driving force to discipline the managers. In a hostile takeover scenario, the raider can bypass the management and could approach the shareholders directly (after appropriate filing with the SEC or MMC), buyout a number of shares under the conditional or unconditional tender offer and acquire the control of the corporation. This is impossible given the ethos and structure of building societies and the regulations governing them. Unlike corporations, a building society is a mutual institution, which does not publicly trade in shares; therefore, the raider cannot overcome the rejection, like the corporations. When an outside institution such as Lloyds Bank first approached the C & G Board of Directors, they were under no obligation to accept their proposal like the board of directors in any hostile takeover bid. But in this case, the Board of Directors had already worked out a merger plan from the management point of view, but certainly without any input from its members. The existing law of the Building Society Commission (BSC) does not require the boards of directors of the building societies to keep the members informed about mergers and takeover bids. Some competitive proposals never see the light of day and, in fact, are rejected without any consultations with the members whom they represent.

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Following the William’s Act 1968 (Senator William of the US Senate), which made takeovers very difficult in the US, a number of changes similar to SEC were adopted by the MMC in the UK for the same purpose. A number of economists and practitioners started questioning the social desirability of such laws. During the Reagan-Thatcher era of liberalisation, there was an outcry for relaxing the anti-trust laws to make takeovers easier. Similar arguments have been offered in the case of C & G, calling for radical changes in the law to make takeovers or floatation of building societies much easier when the original plan for the merger was turned down by the BSC and later, by the High Court.

5.6 Lloyds Bank’s Offer and Response of C & G Members The Monopoly and Mergers Commission and the members of the C & G approved the merger of C & G with Lloyds Bank. An important question to ask is whether C & G members had acted rationally or had suffered the prisoner’s dilemma, in which their self-interest turned out to be less than optimal since they would have been better off by saying ‘no’ to the merger. I will look at the strategy of the members, using some of the results from the earlier chapters. One argument is similar to the one used for corporations by Grossman and Hart (1980). I assume that all the agents, namely, members of the society and management have rational expectations. It is expected that all the agents behave rationally and try to use their strategies in an optimal manner. The theory of takeovers suggests that the raider will not make an offer unless he or she thinks that the target, i.e. the building society, was worth more than what had been offered to its members. Otherwise, the raider cannot make a profit. Hence, there was no economic justification for a takeover bid, given the fact that there is a tangible cost of the takeover process. As I stated earlier in this Chapter, some commentators valued C & G at as much as £2.5 billion, however, the potential value may even be higher. If that is the case, then no rational member of the building society should have voted ‘yes’ to the merger unless they are offered what the society was worth and the takeover should have failed. Like the corporations, they had nothing to fear since the society, being mutual, the raider would have no means for the dilutions of rights of minority shareholders to penalise those who vote ‘no’, in case the takeover was successful.

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What if many members of the society sacrificed the long-term gains for their short-term interests because they received a share of the cash payment and voted ‘yes’ to the merger? Despite this, there were many hurdles, which made the merger task difficult, if not impossible. Under the Building Society’s Act, to win an approval C & G had to pass two stringent test: One and half of all the members (i.e. 50%) entitled to vote, had to give an approval or members holding 90 % of the total balances of eligible investors voted in favour. In addition, 75% of all those who voted, said ‘yes’. In a separate resolution, a simple majority of borrowers also voted ‘yes’. Obviously, voting members excluded from the cash payment motivated by their self-interest may well have voted ‘no’. An estimated 27% of voting investors had been with C & G for less than two years and the ruling of the High Court further excluded 370,000 borrowers who were earlier eligible for cash payment. However, about 20% of borrowers were also savers and benefited under the revised bid. There appeared less certainty about those who were to get the cash but were undecided because of what is known as “incidence of non-tendering” in the takeover literature. Firstly, there was a class of people who were guessing whether they were entitled to cash payments. Such people ensured that others did not benefit either, therefore, may have voted ‘no’. Secondly, given the large membership of C & G, some members lacked knowledge about the takeover and may not have participated in the voting process. Thirdly, there is a class of rich people who just invested in the society for the sake of investing in it. A small cash payment was not going to matter to them. Rather, it would have caused them a great deal of inconvenience for tax purposes; therefore, they would have ignored the whole issue. Fourthly, some people would have speculated about the success of the merger and may well not have participated in the process. However, it became more obvious after the voting process was determined as to who gained from the “incidence of non-tendering”, whether opponents of merger or C & G management. One should also recognise that an earlier attempt by Lloyds Bank to take over Midland Bank for 3.7 billion failed. Perhaps, the offer was not high enough to reflect the market value or credibility of the Lloyds Bank, as an efficient raider was in question. Since the C & G has approved the merger, the theory and the empirical evidence suggests, at least in the mortgage market, it had been a takeover by an inefficient raider. Since the merger had been approved it definitely shows that it benefited the management? It makes one wonder why the management of C & G was so keen on this corporate merger. A recent study by National Institute for Economic and

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Social Research revealed that top directors do more for their pay by promoting takeovers and increasing corporations’ indebtedness than by concentrating on developing their core businesses.

5.7 Formal Model based on Corporate Takeovers This section will involve modelling the takeover of a building society by a bank. The motivation for this model comes from the acquisition of the Cheltenham and Gloucester Building Society by Lloyds Bank plc. The model is not ‘raider specific’. However, any outside institution could be involved in the takeover. The reasons for using a bank are for ease of reference and because, so far, a bank is the only outside institution which has entered the building society sector. A two-stage game will be developed to model this scenario. The first stage will be a decision by nature as to the value of the building society and the subsequent offer by the bank based on this value. The second stage will be the decision by the bank’s members as to whether they vote to accept the offer of the management. An offer from the management of C & G will be considered as synonymous with an offer from the bank since both had agreed that the merger was mutually beneficial and should go ahead with the price offer. The emphasis, therefore, moves to the members of the society, who must indicate whether they were in favour of the merger proposal. Hence, a game between the C & G members and the management was equivalent to one between the Lloyds Bank and the Society’s members. The informational structure of the game is complete but of imperfect information. This is because when a member votes on the proposal, he does so simultaneously with fellow members, whose decision he does not know at the time of making his own decision. This would mean every member of the C & G was in the same information set. To model this situation, with so many different players required to approve the deal at various stages, would prove very complex if all players are taken together. This group of players incorporates the Building Societies Commission, the High Court, the Bank of England and the Lloyds Bank’s shareholders. None of these bodies appear in the game tree. It is assumed that they have consented to the takeover before nature decided the value of the building society, or it is assumed that they are defenceless. This problem can be overcome by assuming that all these bodies had given their approval

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for the merger to go ahead, leaving the decision to the members to approve the merger. For the purposes of modelling, it is also assumed that no competing bids are forthcoming. The game commences with nature moving first and deciding the value of the building society. The choice is made between V=[VH,VL] which represent, respectively, high and low values of the building society, according to a probability distribution given the member’s subjective beliefs about the value of the society. The value, V, takes two extreme values with positive probabilities. Upon the announcement of the offer by the management of C & G for its members, they should decide whether to accept it or not. The necessary majority of the various member groups have already been outlined. Different sections of membership require different majorities to approve the deal. For the purpose of modelling, this process can be simplified by assuming (without loss of generality) a simple majority rule will be sufficient for determining the success of the takeover. Depending upon the value nature has decreed for the building society, the bank will use its strategy to determine what price, p, it will offer. There are many offers the bank might make, its choice being directly affected by the value of the building society, VL or VH and the cost of searching the target, C. This variety of possible offers is indicated in the game tree by the arc of possible prices; for example, see Figure 5, Chapter 3. Upon receiving the offer, members will vote to decide whether the takeover can proceed as planned. In reality, this may involve an extensive ballot of over one million members. For the purposes of modelling, consider a two-stage formulation of a three-person game, which will determine the success or otherwise of the takeover. The choice of the number three is for mathematical simplicity and without loss of generality. If any two of these three members approve the takeover then it is deemed to have succeeded. Members’ voting is represented in the game tree using the concept of an information set. When the first member votes, he is unaware of whether VL or VH is the pertaining value. He must take his decision based solely on the price offered by the bank through management of C & G.

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For simplicity, I use the same notation as that of Chapters 3 and 4. Let: V: Q: n: p:

C: Ȇ

Does the bank or the building society place the value and has an upper bound? Current value of the C & G, in the absence of alternative offer (Q = 0). Number of risk-neutral members of the C & G. Does the bank pay the same amount to each member, if the proposal is approved? It includes any payoffs and bonuses members might get from allowing the building society to give up its mutual status. Let P x n = X, the total amount paid by the bank to the C & G members which is equally divided among its members. Is the cost to the bank of searching the target that meets the criteria for takeover. This sunk cost is irrecoverable. Is the raider’s profit on the transaction.

For a bank to proceed it is necessary that V > p + C otherwise it would not be profitable to takeover. The bank’s profit can be calculated as before. Following on from Chapters 3 and 4, the Lloyds Bank’s strategy is given by IJbijȦ  and each C & G member’s strategy is given by IJn(p). The argument is the price offered by the Lloyds Bank IJbijȦ  The pure strategy and mixed strategies of the players are as defined earlier, but explained in Deman (1999). I proceed straight to the results without replicating every mathematical step. It is trivial to show, for example, see Appendix C, that there exist sequential Nash equilibriums in the subgame. 29 Let us incorporate the rational expectations character into the Nash Equilibrium since both the Bank and the members of the C & G have rational expectations. This would mean, regardless of the realisation of the value of corporation VL or VH, members of the C & G will receive a signal through a price offer about the exact value of the corporation because of one-to-one mapping between p and V. However, in this case, the game will be played only on one side of the tree, as the members of the society know precisely the type of bank since the mortgage market of Lloyds Bank is inefficient. Hence, V=VL implies PL=1. Such an assumption gives us a model parallel to Grossman and Hart’s where they assume that both the raider and the shareholders know the potential value of the corporation. I examine whether some sort of dilution is necessary under these conditions as advocated for a successful takeover.

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Since the realisation of the C & G value is V=VL, then PL=1 and, as in Chapters 3 and 4, simplification will give: A = 1/2 [PL VL + (1-PL)VH - G] = 1/2 (VL-G), and p = (V2L-G2)/4VL, and t(p) = (VL+G)/2VL < 1 It is quite obvious that if G=0, then 2p = VL/2 (i.e. one half the potential value of the C & G). If the Lloyds Bank pays the maximum price to the members of C & G, then it does not make any profits. Rather, the Bank would incur a cost of going through the process of takeover and this cost is sunk as soon as the takeover offer is made. On the other hand, if G > 0, the bank has an incentive to takeover because it pays to the members of C & G less than the potential value of the corporation. The bank makes positive profits if and only if G > C. Hence, from proposition 7 of the earlier Chapters, it is clear that if the bank is restricted to a conditional takeover bid for all members of the C & G (i.e. unanimity), a symmetric equilibrium exists at a price p = A, and all members will say ‘yes’ to the offer with probability 1. Hence, there exist separating equilibriums in the subgame and the bank succeeds. Hence, one cannot rule out the possibility of a takeover by an inefficient raider. However, there was no provision for dilution and there is no mechanism by which the bank can punish those who did not vote in favour of the takeover. In fact, such a provision becomes unnecessary in a game of finite players, therefore, substitute G = 0 and analyse the equilibriums. It is straightforward that p = VL/4, and IJn(p) = VL/4A < 1. We have seen from Proposition 9 of previous results that the difference between the banks’ profits in the mixed strategy symmetric equilibrium and in the pure strategy symmetric equilibrium, are positive. Hence, the Bank was better off by not rewarding every member of the C & G and yet can succeed in taking control of the C & G. I believe this adequately characterises the process of the voting behaviour of C & G members. However, the decision of the members of C & G to say ‘yes’ is sub-optimal because ex-ante there was no indication that they would be better off after the merger with a bank who was not doing very well in the mortgage market. However, it is clear that the degree of success and the level of profit the bank can expect depend, crucially, on the divergence between, what he expects the building society to be worth V and what he has to pay for it V-. If the merger goes ahead, this is equilibrium in the game when the takeover succeeds.

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5.8 Introduction of a Prime Rate It is, therefore, necessary to introduce a mechanism by which a bank can reward those who vote in favour of the takeover, or punish those who vote against the takeover if the raider is to gain the 75% required. A possible solution might be the offer of a ‘prime rate’ of interest to those who have voted in favour of the proposal. That is, a rate of interest higher than what would normally be paid on a member’s account. It is assumed here that the bank can distinguish between those who voted in favour of the merger and those who voted against it, a reasonable assumption when the game is played with a finite number of players. A similar mechanism may be used to try and persuade borrowers to approve the takeover. By offering a lower mortgage rate to those who vote for the takeover, the bank can punish those who are against it. The notion of the prime rate can be used as synonymous with dilution to calculate the payoff of the bank and the members of C & G, as we did in Chapters 3 and 4. Hence, on the basis of the discussion above, it is clear that the bank’s payoff when the vote is unanimous, and when two of the three members vote ‘yes’ can be compared. When all the members respond positively, the bank must pay 3p+C. When one of the members votes ‘no’, the bank must pay less because it does not have to offer an advantage of a prime rate to he who said ‘no’. Under this scenario, because of the difference equivalent to the prime rate, it is to the bank’s advantage if less than 100 %, but a majority of the members, approve the deal. This can be compared to the same situation in a corporation. A raider, who is attempting a takeover, will not usually purchase 100% of the shares. If he needs 50% to gain control, he will only buy this amount. An optimal decision for the raider may, therefore, be not to buy 100% of the shares, but instead to buy just enough shares to gain control of the corporation. A similar analysis can be carried out for this building society model. From the raider’s perspective, the optimal voting strategy of the members is for 75% to approve the takeover and 25% to refuse it. Hence, he will pay p to 75% of the members and less to 25% of them who failed to say ‘yes’. He would like just enough members to approve the deal for him to gain control. If more than 75% of the voting members sanction the takeover, the bank could distribute the amount he had set aside for payment of the prime rate on a pro rata basis. This option fixes the amount the bank has to pay to the members and makes the number of members who approve the takeover

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irrelevant to him. It might, however, also be considered less of an incentive for them to approve the deal. It is likely, if the takeover is to proceed, more than 75% will vote in favour of it, i.e. there is a negligible chance that exactly 75% will sanction the deal. Therefore, if the deal proceeds, each member can expect to receive a lower amount on a pro rata basis than under a specified prime rate basis. In this way, it may appeal less to members as an incentive and have less influence on their vote. The bank may favour the pro rata scheme as it enables it to know in advance how much it will pay those members who vote in its favour. It should be stressed that the prime rate is only an example of an incentive package, which might be presented to the members of a society. It may be difficult to implement in practice. Despite this, the theory is sound, and an additional incentive of some kind is necessary to persuade members to sanction the takeover. This could conceivably take any form. All that is required is something which is attractive to members; something that would influence them to vote in favour of the raider. The above mechanism is not a description of the actual process but only a suggestion, as stated earlier. I will discuss the conclusion in the next chapter.

CHAPTER 6 CONCLUSIONS

Game theory has emerged as one of the most powerful techniques of analysis because, in the game, both players are actively trying to promote their own welfare in opposition to that of the opponent. It develops rational criteria for selecting a strategy in which each player will uncompromisingly attempt to do as well as possible in relation to his opponent by giving the best response. However, game theory is often criticised on the grounds that it is sensitive to minor changes in the assumptions and lacks empirical verification. The existence of various equilibriums depends on what information is available to players or who moves first. Deman (1987) basically identifies three criteria for a theory to be considered as useful if it (i) is consistent with known facts; ii) provides greater insights and understanding than earlier theories; and (iii) can be used for forecasting future trends, particularly under the conditions that differ from the past. The underlying assumption is that both theorists and empiricists have common objectives to describe, explain, relate, anticipate, evaluate phenomena, events, and relationships crucial to decision- making through the theory construction and data collection. Unfortunately, crucial variables are hard to measure, but that does not diminish their importance. As Rasmussen (1992) pointed out, “the economist’s empirical work has dominated case-by-case verification replacing the traditional regression-running.” A theory’s sensitivity to assumptions is not a shortcoming. Rather, it is a contribution of the theory, pointing out the important role of what were once thought to be insignificant details of reality in the world. To blame game theory for any failure to predict or selfishness is like blaming a cardiologist for heart disease. Failure of the macroeconomic forecasts, and the growing importance of the microeconomic theory of the firm have brought game theory to the forefront of economic decision-making. It provides new insights, not suggested by other approaches. Rasmussen (1992) concluded, “Just as marginalism is more than the application of calculus to old problems in economics, so the game theory is as important for changing the agenda as for introducing new techniques.”

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In Chapter 3, I reconsidered Grossman and Hart’s earlier work on corporate takeovers using a game-theoretic framework and identified mixed strategy equilibriums. In their model, dilution is necessary for a takeover to be successful and to rule out the free-rider’s problem, and there is no limit on such a dilution factor. Conversely, I have shown that the free-rider problem does not exist in extreme cases of pure strategy equilibrium, and that takeover is possible with or without dilution. Although Grossman and Hart claim that their theory rules out the takeover by the inefficient raider, in which the shareholders who sell are worse off than they would be otherwise, I have shown that such possibilities are not ruled out. In fact, their argument relies on some rather arbitrary assumptions that there are only pure strategy equilibriums and the inability of the inefficient raider to succeed. Furthermore, our study of the changes in the dilution factor reveals that Grossman and Hart have been more optimistic about the welfare consequences of hostile takeovers than is really justified by their theoretical model. I conjecture that Grossman and Hart’s type of pure strategy equilibriums are possible only if the decisions are unanimous. This is more likely to happen in the case of takeover of the urban property in the real estate market, for example, Deman and Wen (1994). Bagnoli and Lipman (1988), Hirshleifer and Titman (1990), Deman 1991, 1994, 1999, 2000) have argued that the Grossman and Hart characterisation of the real world of pure strategy equilibriums seems to be unrealistic. In Chapter 4, I applied a game-theoretic model to urban renewal via property takeovers, and have shown that there exist pure strategy symmetric equilibriums. Hence, the extreme cases of pure strategy equilibriums are more likely to be found in real estate takeovers than in the market for corporate control. The assumption of either impotent managers or complete absence of management is also more consistent with the real estate market than the market for corporate control. I have developed a game-theoretic model of urban property takeovers to show that it is possible to realise these pure strategy symmetric equilibriums in the real world. Furthermore, a coherent approach to interference by way of exercising the right of eminent domain has been discussed. The possibility of taking over urban property or plots of land by an inefficient developer in the name of either urban renewal or site assembly is not completely ruled out. Hence, the applications of eminent domain, such as urban renewal, are often either (i) socially inefficient, but beneficial to selected individuals or group at the expense of others; or are (ii) socially inefficient because the owners are truly harmed by the use of eminent domain if their dwelling and surrounding neighbourhood

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are really worth to them more than the “just compensation” allowed by the courts. At the end of this chapter, I have also discussed comparative static of various parameters, including an optimal limit on the eminent domain in cases where any holdout problem exists. A generalisation of such a model is not difficult, but preliminary results may be useful in formulating public policies regarding privatisation of urban renewal efforts. In Chapter 5, I discussed a potential application of the takeover model to building societies. There is a wide range of applications of the takeover model of corporate finance to other sectors of the economy; for example, mergers of banks, building societies, hospital services, and academic institutions, etc. In a growing financial market, many activities of the other sectors of the economy are publicly quoted on the stock exchange. Hence, application of takeover models and game theory can serve as an important tool for formulating public policy. Following from the analysis in Chapter 5, a possible suggestion is that a new building society could incorporate into its charter permission for any raider to pay a prime rate to those members who sanction his approach to take over the building society. This would hopefully have the effect of encouraging management to run the building society efficiently, for fear of losing their control over it. Effectively, it introduces a costless method of monitoring management. The introduction of a prime rate has the same effect as the dilution factor used by Grossman and Hart (1980) in their paper. The obvious objection to such a clause being introduced into the charter of a building society will come from the society’s board, which may feel it leaves them vulnerable to takeover. They may also fear their members will be unduly influenced by the tangible benefits which will flow to them, and thus agree to any takeover attempt, regardless of whether it is to the benefit of their society in the long run. These fears are well-founded but can be easily overcome. The board of any building society may simply reject takeover bids, no matter how inefficiently they are running the society. Eventually, however, a society, which is being run poorly, will suffer BSC intervention or a motion by its members to change the board of directors. This ‘inefficiency’ theory cannot be suitably applied to the case of Cheltenham and Gloucester Building Society and Lloyds Bank. Although the introduction of a prime rate would ensure the board acted efficiently, the board of Cheltenham and Gloucester seems to be managing without it. As stated already, it is one of the most cost-efficient building societies operating in the UK, and so was not a takeover target for reasons of

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inefficiency. Nevertheless, a prime rate would act as a safety net for members if their board failed to maintain their level of efficiency and act in their self-interests. Several obstacles stand in the way of the introduction of such a mechanism. The game in Chapter 5 is a vast simplification of reality. Even if the Building Society Commission agreed to its introduction in principle, it may prove logistically impossible. It relies heavily on the raiding institution being able to identify how each member of the society voted in the ballot on the takeover. Cheltenham and Gloucester have 1.3 million members and is rated as the sixth largest society operating in the UK. Others would find such a mechanism even harder to operate. It could also cause disenchantment among members who feel they acted in the interests of their society in voting against the takeover. There is nothing to prevent such members leaving and investing in, or borrowing from, a rival society. It could be argued that the members of Cheltenham and Gloucester should have resisted the Lloyds bid, as that Building Society is already extremely efficient. The tangible cash benefits to members, however, are an overriding factor in swaying many of them to accept the bid. They may also feel that Lloyds’ reputation means they are putting their Society in safe hands. Lloyds has a good efficiency record in comparison with other leading retail banks with the exception of the mortgage market. Concentration in the building society sector is likely to continue for the foreseeable future. There are still 84 societies operating in the UK, and many of the local and regional operations may find themselves becoming part of their national counterparts. One can only guess when the trend of mergers and transfers of engagements will come to an end —whether Lloyds Bank has opened the path for other retail banks to follow them into the building society sector remains to be seen. Many will have been interested to see the case in the High Court, testing the water for possible takeovers. The other retail banks can wait and see if the Lloyds move proves to be a success and can then enter the sector. There is no shortage of possible targets, but some of the other national societies may be less willing than Cheltenham and Gloucester to bow to a takeover. Future research on this topic could be directed in two areas. Firstly, an extension of the game introduced here is a possibility. A game with a more complicated structure could be introduced and solved, possibly modelling the conflict, which exists between long-standing members, new members, and borrowers. Secondly, research can be carried out to establish how the

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results of Cheltenham and Gloucester plc compare to its mutual ancestor. It is possible the public will perceive it differently, now that it is linked to one of the unpopular retail banks. Efficiency levels may suffer or be enhanced by the wider market and cheaper funds now available to it. I also see two variations of the takeover model. A takeover always occurs in the first variation of the model. However, in the second variation, suppose that the raider can only make one attempt to buy shares (i.e. one-shot game) and that the raider becomes just another shareholder (large) under the incumbent management if the takeover bid is unsuccessful or when a “partial” tender offer is made. As an unsuccessful raider (large minority shareholder), the raider will be in a strong position to attempt another offer, it is relevant to examine the effect of past failures on the raider’s preferences as to how generous an initial tender offer he should make that is acceptable to shareholders in order to take over the corporation. An element of the theory of bargaining can be used to explain this. Although the merger wave of the 1980s was marked by the new sources of transactions and emergence of new organisational forms facilitated by innovations in financing techniques, an increasingly important type of corporate restructuring in the UK has been the management buy-out. Wright, Wilson, Robbies, and Ennew (1996) examine management buy-out failures using both financial and non-financial information. In fact, research in the area of management buy-outs and the shareholders’ activism has been gaining momentum in the 1990s.

APPENDIX A MATHEMATICAL NOTATIONS In this appendix, I define a number of variables and explain mathematical notations to identify strategies of the raider and the shareholders along with their respective beliefs.

V:

the potential value of the corporation under the raider’s management, and has an upper bound.

C:

a cost of searching the target.

Q:

Status quo or current value of the corporation’s shares under the incumbent management.

k:

# of risk-neutral shareholders, each holding one share. There is a continuum of shareholders each with one share.

G:

maximum dilution possible by the raider of the minority shareholders, if takeover is successful.

V 112 :

probability of beliefs of shareholder 1 about the shareholder 2’s strategy.

V 221 V 221 :

probabilities of beliefs of shareholder 2 about the shareholder 1’s strategy.

V1:

Shareholder 1’s strategy of tendering.

V2:

Shareholder 2’s strategy of tendering.

V 01 :

Shareholder 1’s equilibrium strategy.

Game Theory and Its Applications to Takeovers

V 02 :

Shareholder 2’s equilibrium strategy.

::

Sample space.

E:

Sigma-Algebra.

107

APPENDIX B-1 GLOSSARY OF TERMS

The Language of Corporate Takeovers ANY-OR-ALL-TENDER OFFER: The bidder or raider will buy any tendered shares of the target corporation as long as the conditions of a minimum number of tendered shares are met to ensure majority control after the offer. CONDITIONAL TENDER OFFER: In this offer, the raider specifies a maximum number of shares to be purchased in addition to the minimum required. If the bid is oversubscribed, the tendered share becomes subject to pro-rationing. This tender offer is further sub-divided into two-tier negotiated, non-negotiated and partial tender offers. CROWN JEWEL: It is the most valued asset held by an acquisition target and divestiture of this asset is frequently a sufficient defence to discourage the takeover of the corporation. DILUTION FACTOR: To the extent, the value of minority shareholders is diluted after takeover of the corporation. The Securities and Exchange Commission prohibits it. Since shareholders will not tender their shares for less than the expected post-takeover value of their shares to them, a divergence must be created between this value and the value of the shares to the raider. This difference in the value of the shares is called dilution. The provision of dilution factor has the effect of lowering the acquisition price and permits the raider to exclude minority shareholders from receiving the gains in the value of their shares produced by taking over mechanism, in other words, excluding the free riders. FAIR PRICE-AMENDMENT: It requires super-majority approval of non-uniform or two-tier tender offers. Takeover bids not approved by the Board of Directors can be avoided by a uniform bid for less than all outstanding shares (if the bid is oversubscribed, it is subjected to prorating.

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FRIENDLY TAKEOVER: Sometimes referred to as Merger or Synergistic Takeover and it occurs when an acquiring firm referred to as bidder or raider and target firm agreed to combine their businesses to realise the benefits. Synergistic gains can accrue to the corporation from consolidation of research and development labs or of market networks. Merger proposals require the approval of the managers (Board of Directors) of the target corporation. GOLDEN PARACHUTES: The provisions in the employment contracts of top-level executives that provide for severance pay or other compensation should they lose their job as a result of a hostile takeover. GREENMAIL: The premium paid by a targeted company to a raider or bidder in exchange for his acquired shares of the targeted company. HOSTILE TAKEOVERS: Also, called disciplinary takeovers in the literature. The purpose of such takeovers seems to correct non-value-maximising practices of managers of the target corporations. Takeover proposals do not need the approval of the managers of the target corporation. In fact, they are made directly to the shareholders of the target. INTER-FIRM TENDER OFFER: The separation of ownership and control in large corporations led to the development of the inter-firm tender offer as an important vehicle and became a popular mechanism for transfer of ownership. INTRA-FIRM TENDER OFFER: Prior to 1960s, the so-called intra-firm tender offer was used exclusively to acquire shares in the issuers repurchase program. KICK IN THE PANTS: New information induces the incumbent management to implement a higher-valued strategy on its own. LEVERAGED BUYOUT: The purchase of publicly owned company’s stocks by the incumbent management with a portion of the purchase price financed by outside investors. The company is de-listed and public trading in the stock ceases. LOCKUP DEFENSE: Gives a friendly party (i.e. White Knight) the right to purchase assets of the corporation, in particular, the crown jewel, thus discouraging a takeover attempt by the raider.

110

Appendix B-1

MAIDEN: A term sometimes used to refer to the company at which the takeover is directed by the raider or bidder. MANAGEMENT BUY-OUT: It occurs when a management team within a corporation or division purchases that corporation from its current owners, thus becoming owner-managers. It is prevalent in both the private-public sectors and is one means by which privatisation may take place. NEGOTIATED TWO-TIER TENDER OFFER: The bidder or raider, at the time of the first-tier offer, agrees with target management on the terms of the subsequent merger. NON-NEGOTIATED TWO-TIER TENDER OFFER: No terms are agreed to at the time of the original offer for control of the corporation. It lies between the pure partial offer and non-negotiated two-tier tender offer. POISON PILL: It is used as a takeover defence by the incumbent management, which gives stockholders other than those, involved in a hostile takeover the right to purchase securities at a very favourable price in the event of a takeover bid. PRIVATISATION: The purchase of publicly owned company’s stocks by the incumbent or another competing management group. The company is de-listed and public trading in the stock ceases. PRORATIONING: If the number of shares tendered in a takeover bid are more than required by a conditional offer (i.e. if the bid is oversubscribed), then the raider will buy the same proportion of shares from everyone who tendered. PROXY CONTEST: The solicitation of stockholder votes generally for the purpose of electing a slate of directors in competition with the current directors to change the composition. PURE PARTIAL TENDER OFFER: It is defined as one in which there is no announced second-tier offer during the tender offer and no clean-up merger or tender offer closely following the execution of the tender offer. Partial Offers are commonly used for less than 50 percent control of ownership in the corporation. RAIDER OR BIDDER: The person(s) or corporation who identifies the potential target and attempts to takeover.

Game Theory and Its Applications to Takeovers

111

SHARK REPELLANT: Anti-takeover corporate charter amendments such as staggered terms for directors, super-majority requirement for approving the merger, or mandate that bidders pay the same price for all shares in a buyout. SITTING ON THE GOLDMINE: The dissemination of the new information prompts the market to revalue previously ‘undervalued’ target shares. STANDSTILL AGREEMENT: A contract in which a raider or corporation agrees to limit its holdings in the target corporation and not make a takeover attempt. STRIPPER: A successful raider who, once the target is acquired, sells off some of the assets of the target company to destroy its original entity. TAKEOVER: The word “takeover” is used in as a generic term to refer to any acquisition through a tender offer. In layman’s language, it is a straightforward transaction in which two firms decide to combine their assets either in a friendly or unfriendly manner under established legal procedures. TARGET: The potential corporation at which the takeover attempt is directed. TARGETED REPURCHASE: A repurchase of common stock from an individual holder or a tender repurchase that excludes an individual holder. The former is the most frequent form of greenmail, while the latter is a common defensive tactic against the takeover. TENDER OFFER: An offer by bidder or raider directly made to shareholders to buy some or all of their shares for a specified price during a specified time. Unlike merger proposals, any tender offers for takeovers are made and successfully executed over the expressed objections of the target management. TWO-TIER TENDER OFFER: A takeover offer that provides a cash and non-cash price in two steps. In the first step, cash price offer for sufficient shares to obtain control of the corporation, then in the second step, a lower non-cash (securities) price offered for the remaining shares. WHITE KNIGHT: A merger partner solicited by the management of a target corporation who offers an alternative merger plan to that offered by the raider which protects the target company from the takeover.

APPENDIX B-2 GLOSSARY OF TERMS

The Language of the Game Theory CLOSE CIRCLE: Termination node. GAME OF COMPLETE INFORMATION: If each player knows (N, Y, p, I, q), it is a game of complete information otherwise incomplete information. GAME OF INCOMPLETE INFORMATION: It is a game in which, at the first point in time when the players can begin to plan their moves in the game, some players already have private information about the game that other players do not have. GAME THEORY: It develops a “rational criteria for selecting a strategy”. In the game, both players are rational and each player will uncompromisingly attempt to do as well as possible relative to his opponent. In other words, in game theory, both players (shareholders and the raider) are actively trying to promote their own welfare in opposition to that of the opponent. GAME OF PERFECT INFORMATION: If each information set contains only one node, then it is a game of perfect information, otherwise it is a game of imperfect information. GAME: In the language of game theory, a game refers to any social situation involving two or more individuals. *(N,Y, p, I,q) is a finite game in extensive form, where, N = Number of players, Y = Tree, p = payoffs, I = Information Set, q = Probabilities. INFORMATION SET: At the nodes within the same information set players do not know at which node they are. MIXED STRATEGY EQUILIBRIUM: The concept of mixed strategy equilibrium is a limit of equilibriums where each player’s payoffs are

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randomly perturbed by a small amount unobservable to his opponent. MIXED STRATEGY SYMMETRIC EQUILIBRIUM: Symmetry means shareholders who are identically situated or have same beliefs (holding the same number of shares or conjecture about the opponent) behave identically. Symmetry also implies that expected payoffs are equal so that all shareholders are treated the same way. NASH EQUILIBRIUM: A profile of strategy forms Nash Equilibrium if each player’s strategy is an optimal response to the other player’s strategy. NON-COOPERATION: It is a game in which there are no possibilities for communication, correlation or precommitment. In equilibrium, each player in the game independently chooses a strategy in a way that maximises his payoff. OPEN CIRCLE: Decision node. PERFECT SEQUENTIAL EQUILIBRIUM: Sequentially perfection requires a strategy to be the best response to any belief, `including beliefs that will not emerge in equilibrium. PURE STRATEGY EQUILIBRIUM: Each player uses his unique best response. In equilibrium, either all shareholders tender their shares with certainty or they do not tender with certainty and the raid is successful with probability one or zero, respectively. SUBGAME PERFECT EQUILIBRIUM: A subgame perfect equilibrium was defined for extensive form games with complete but imperfect information. A strategy profile is subgame perfect if each player’s strategy remains the best response to other players’ strategies in every proper subgame that are not expected to be reached. This is a more restrictive equilibrium concept for games in an extensive form called subgame perfect, which strengthens the notion of being an optimal response.

APPENDIX C

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ENDNOTES

1

Economic Analysis of takeovers has identified mainly two broad classes of models, namely: disciplinary and synergistic, which are also called hostile and friendly takeovers, respectively in the literature, see Fishman (1986). I do not consider the latter, that uses the atomistic shareholders’ assumption quite differently. Furthermore, there are papers by Shleifer and Vishny (1986), Bebchuk (1984), Hirshleifer and Titman (1990), etc., which do not assume atomistic shareholders.

2

If, however, all shareholders are rational decision-makers, then they also realise that they will not be able to obtain this increased anticipated value unless the “raider” can gain control of the voting rights in their shares. This would be a sufficient inducement for a majority of share-holders to tender their shares, especially in the light of the existence of a probability distribution regarding the “presumed fact” that the “raider” is more competent than current management. I appreciate the anonymous referee for pointing this out to me. 3

See, for example, Grossman and Hart (1980a), and Bradley and Kim (1985).

4

See, for example, Grossman and Hart (1980b), p. 43.

5 See, Grossman and Hart (1980b) for an analysis of how monetary levels of dilution are related to the stringency of disclosure and appraisal requirements. 6

Actual corporate charters specify the extent to which minority shareholders are protected from dilution, see page 46, Grossman and Hart (1980a). 7

See, for example, Shleifer and Vishny (1986).

8

Grossman and Hart (1980a), p. 59.

9 I came across two papers by Bagnoli and Lipman (1988) and Shleifer and Titman (1989) showing mixed strategy equilibriums. However, assumptions of their models are quite different from Grossman and Hart (see, Chapter 2). An earlier paper by Kovenock (1984) also shows mixed strategy sub-game equilibrium, as shown by Bagnoli and Lipman, but he does not consider an optimal strategy of the raider. 10 The assumption of atomistic shareholder implies that each shareholder has measure zero. Hence, I assume that shareholders’ strategies do not respond to deviation by a single shareholder.

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11

For example, see Grossman and Hart (1980a). However, Bagnoli and Lipman (1988) allow a shareholder to hold more than one share of stock, and their model uses different assumptions in the game for the finite stockholders. Thus, they changed the original assumptions of Grossman and Hart’s model. The profit equation also appears to be somewhat arbitrary in their model.

12

See, for example, Grossman and Hart (1980a). I assume a single potential raider, the impotence of management, and only one realisation process in the takeover process. 13

I am not suggesting that the corporation becomes valueless if the raid is unsuccessful. I am simply assigning Q = 0 for mathematical simplicity. Hence, the potential value of the corporation is [0 < V < 1]. 14

Unacquired shares and non-tendering shareholders in a successful takeover bid fall roughly into three groups: (i) those who did not get adequate opportunity to do so because they were not aware of the takeover bid or were unable to tender their shares in time; (ii) those who did not tender because they viewed the status-quo per share value of the corporation’s share higher than the tender offer, i.e. p < Q/k and from the initial expectation that the takeover bid will fail; and (iii) for tax reasons. 15 A study by the Office of the Chief Economist, Securities and Exchange Commission, The Economics of Any-or-all, Partial and Two-Tier Tender Offers, Table 9 (April 15, 1985). There is a substantial incidence of non-tendering in successful takeover bids of all kinds, that is, whether the takeover bid is for any-or-all shares or partial, and whether or not it is expected to be followed by an immediate takeover. I refer to SEC because Grossman and Hart’s paper is based on the US experience. 16

Actually, C does not do anything in our model and I may drop it from the model. However, Grossman and Hart (1980a) realised that cost becomes important in analysis if it is made stochastic in the model. 17 Because of imperfect competition in the real estate market and transaction costs, whichever developer can appropriate more gains over the other becomes the acquirer. The one-acquirer argument is also consistent because of ex-ante costs of research and information in the takeover process, which is sunk by the time the takeover occurs. This limits the ex-post competition among the developers if one developer is the first to understand how the particular project has to be carried out in a socially efficient way, so that he can make profits. Since the other developers do not have this information, they cannot compete with the informed developer. 18 The assumption of zero demolition cost is realistic if the developer is only interested in renovating the existing structure of the property in question.

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19

See, for example, Grossman and Hart (1980). Here atomistic means that no individual homeowner or landowner can influence the outcome of the takeover process.

20 There is no such term as “dilution” in the urban economics literature. However, we are using this term much as it is used in the literature on corporate finance. Dilution is the extent to which the initial residents are forced to sell to the developer or comply with the new standards of the development. Such dilution is possible through the use of zoning ordinances and building codes. Dilution increases the costs to potential holdouts. 21 In eqXLOLEULXPWKHGHYHORSHU¶VSURILWVDUHJLYHQE\ʌ 9 -2p-C. On substituting for p L = 1/2 (VL-Ĭ ZHJHWʌ Ĭ- &)RUʌ!LWLVQHFHVVDU\WKDWĬ!& 22

Grossman and Hart argue that the use of unanimity rule does not occur in takeovers of widely held corporations, because each stockholder would try to be the only “holdout” and thus anticipate a secret payment from the raider for his stocks, in addition to the tender offer price. 23

I worked out profit and price equations for n=3 players by replacing t by x in equation #10 to analyse the equilibriums. The solution by Mathematica gives me one positive root, i.e. the probability of takeover. For results, see Appendix. 24 Actually, C does not do anything in our model and we may drop it from the model. However, cost becomes important in analysis if it is made stochastic in the model. 25 We are ignoring the lemon problem in order to keep the model as simple as possible. Coase’s (1960) arguments imply that if there are no transactions costs, owners will agree to improve their property to a level maximising their joint profits. However, zero transaction cost is too strong an assumption. 26

We are assuming that there is no distributional effect, i.e. transfer of wealth from homeowners to the developer or vice-versa. Hence, we are looking at a Pareto improvement case rather than a rent-seeking problem. 27 It is a matter of record, Lloyds has tried and failed in the past to buy Royal Bank of Scotland, Standard Chartered and Midland Bank. 28 Barnes (1985) provides evidence to suggest that the level of member participation is, on average, very low. Formation of a coalition is not costless and the democratic rule made it very difficult to form a coalition against the incumbent management. 29 If we plug in k=3 (members of the Building Society), dilution = 0 and replace sigma with X in equation 10 (a) & 10(b). Substitution of 10(a) into 10(b) will give a cubic equation. A solution to the cubic equation by Mathematica gives three roots. To show equilibrium, I have to demonstrate that one of the roots is positive and less

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than 1 (sigmas being probabilities). Results in Appendix C show that. In general, results are true for k=n players. Please note that X in the equation in Appendix C is different from the one used for notation in this equation.