Incentive Scoring Mechanism Design in Battle Royale Games 9781450385084

Table of contents :
Abstract
1 INTRODUCTION
2 RELATED WORKS
3 BATTLE ROYALE GAMES AND PUBG
4 THE GRAPH-BASED MECHANISMS
5 EXPERIMENTS
5.1 Experiment Design
5.2 Simulation Results
6 CONCLUSION
References

Citation preview

Incentive Scoring Mechanism Design in Battle Royale Games Qi Shi

Shuai Mao

Dong Hao

University of Electronic Science and Technology of China, China

University of Electronic Science and Technology of China, China

University of Electronic Science and Technology of China, China

ABSTRACT

of the rank-based ‘knockout + surviving’ scoring mechanism, calculate scores for knockout and for surviving time separately to achieve incentive. Our simulating experiments show that, it gives little incentive, and is unfair enough for the teams with high skill levels in the game. We additionally raise three graph-based scoring mechanisms, including an instance of the PageRank algorithm, which show a stronger incentive for high-skill-level teams, while keeping a similar performance in ranking the teams. Experimental results also indicate that, one of the scoring mechanisms we raise can be used for estimating the teams’ skill levels with the scoring results, where skill levels have numerical relations to the teams’ winning probabilities.

Battle Royale games are popular among players in recent years. The mainstream Battle Royale games utilize a rank-based scoring mechanism which calculates scores for knockout and for surviving time separately. However, our simulating experiments show that the currently used mechanism has little incentive for the highskill-level teams, which is unfair and may discourage those teams. Besides, we raise three graph-based mechanisms to overcome this shortcoming while keeping a similar performance in ranking the teams. Experimental results also show that one of the mechanisms we raise can also be used for evaluating the skill of all teams.

CCS CONCEPTS

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• Human-centered computing; • Interaction design theory, concepts and paradigms;

Reward designing is an important aspect of game designing. Reward systems can be viewed as player motivators and provide positive experiences to players [1]. Scoring acts as a type of positive feedback and reward system, capable of spurring players on toward greater challenges [2]. Different genres of games can apply scoring systems with different traits to achieve their special purposes [3]. For instance, designers can encourage players to keep contributing in games by applying a scoring system that is able to smooth the learning curve of players [4]. An overview of the gameplay style and characteristics of Battle Royale games is given in [5], but agentbased simulating results find that the outcomes of Battle Royale games are only weakly aligned with actual player skills [6]. Born of fiction and movie [7], Battle Royale is going beyond video games to describe a more general competing mode of a system. Reference [8] applies this term to describe the competition among countries; [9] raises an optimization approach inspired by Battle Royale games. Though some works on performance evaluation have been down in the sports field [10, 11], which can be extended to the genre of games where two teams of players compete in each game, there is no published research on performance evaluation or scoring mechanism in Battle Royale system as far as we know. Even so, evaluating many items in a system is not new to the world. For instance, PageRank [12, 13] is a well-known algorithm for assigning weight to webpages according to web structure determined by the hyperlinks among them. It is also used as a network centrality measure that help understanding the graph better by analyzing the importance of each node in light of the entire graph structure [14]. As a tool of evaluating items in a system with network structure, applications of PageRank algorithm extend to many other fields such as biology, chemistry, ecology, neuroscience, physics, sports, and computer systems [15].

KEYWORDS Scoring system, Battle royale games, Mechanism design ACM Reference Format: Qi Shi, Shuai Mao, and Dong Hao. 2021. Incentive Scoring Mechanism Design in Battle Royale Games. In 2021 The 5th International Conference on Algorithms, Computing and Systems (ICACS ’21), September 24–26, 2021, Xi’an, China. ACM, New York, NY, USA, 7 pages. https://doi.org/10.1145/ 3490700.3490703

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RELATED WORKS

INTRODUCTION

Battle Royale game, such as Fortnite Battle Royale, Apex Legends, Player Unknown’s Battlegrounds and so on, is a class of game that involves dozens of teams, who start with minimal equipment and must eliminate all other teams while avoiding being trapped outside of a shrinking ‘safe area’. The team surviving to the last is defined as winner. In a common sense, there is a unique winner in a Battle Royale game. However, in some occasions it is required to evaluate every team, such as in the matches. Scoring systems are used to achieve such a requirement. Moreover, scoring systems are also designed for incentivizing players in games, where fairness is a key property that better performance in game should be worthy of higher score. In Battle Royale games, players are encouraged to eliminate as more rivals as possible to be the last survival. The currently used scoring systems in most Battle Royale games, which are instances Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]. ICACS ’21, September 24–26, 2021, Xi’an, China © 2021 Association for Computing Machinery. ACM ISBN 978-1-4503-8508-4/21/09. . . $15.00 https://doi.org/10.1145/3490700.3490703

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BATTLE ROYALE GAMES AND PUBG

As a genre of video games, Battle Royale game takes its name from the Japanese film Battle Royale and represents a type of last-manstanding competition in a shrinking play zone. There are a lot

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According to the scoring system described before, scores of all teams in Table 1 are as Table 2 showing.

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Table 1: An example of one game, where 16 teams compete. In each time slice, the team with shadowed-

Table 1: An example of one game, where 16 teams compete. In each time slice, the team with shadowed-background ID elimID eliminates with strikethrough ID.the The ‘Rank’ columninshows ID of theand team inates thebackground team with strikethrough ID.the Theteam ‘Rank’ column shows ID of team eliminated this time slice its rank in � eliminated in this time slice and its rank in the reversed elimination sequence. Team with underlined the reversed elimination sequence. Team m with underlined ID is non-combat eliminated in time slice 6.

ID is non-combat eliminated in time slice 6.

Time Slice 0 1 2 3 4 5 6 7

Alive Teams abcdefghijklmnop abcdefghijklmnop abcdefghijklmnop abcdefghijklmnop abcdefghijklmnop abcdefghijklmnop abcdefghijklmnop abcdefghijklmnop

Rank h: 16 o: 15 p:14 j: 13 f: 12 c: 11 m: 10 l: 9

Time Slice 8 9 10 11 12 13 14 15

Alive Teams abcdefghijklmnop abcdefghijklmnop abcdefghijklmnop abcdefghijklmnop abcdefghijklmnop abcdefghijklmnop abcdefghijklmnop abcdefghijklmnop

Rank a: 8 k: 7 e: 6 n: 5 b: 4 d: 3 i: 2 g: 1

Table 2:belonging The scores in the game shown Table in PUBG Professional of video games to this genre, all of whichin utilize the1 usingwethe saycurrent the team scoring ranks i th system in this game for short. The team ranking League, under the assumption that there's only one player in each team. rank-based ‘knockout + surviving’ scoring mechanism. Within all first is the winner and survives to the end. Let’s see an example. of the Battle Royale games, PUBG, short for Player Unknown’s Suppose that a game among 16 teams labelled a − p, with only one Rank Rank Point Point Total Score Team in each Rankteam, Rank Point inKnockout Point Totalelimination Score BattleTeam Grounds, is one of the mostKnockout well-known and has a mature player is shown Table 1. The reversed g 1 10 research, we4 shall take the scoring 14 l 0 д, i, d, b, n, e,1k, a, l, m, c, f 1, j, p, o, h. Professional League. In this sequence in 9this game is system iin the PUBG Professional League,1 a popular instance According to the scoring before, scores of all 2 6 7 of m 10 0 system described 1 1 the ‘knockout + surviving’ as our analyzing teams d 3 5 scoring mechanism 0 5 c in Table 11 1 are as0Table 2 showing. 0 0 baseline, accepted 8by the b since 4it is clearly 4 stated and generally 4 f 12 0 0 0 players.n 4 j THE 13 GRAPH-BASED MECHANISMS 5 3 1 4 0 0 0 In each are divided 1into teams, with at e PUBG 6 game, players 2 3 most 14 that, in 0 a Battle Royale 0 game, a team can 0 only be Wephave noticed four players in each team. All players are set to be unarmed and eliminated by or a ‘non-combat’ factor, which k 7 1 1 2 o 15 another team 0 0 0 means, parachute from a flight at the beginning. The players can choose theheliminating When a 8 1 0 1 16 relation0is a kind of unary 0 or binary relation. 0 wherever to land on the given map and search for weapons to we artificially remove the condition when two teams eliminate prepare for combats. Players usually scatter around the map at first, each other, we can denote all the eliminating relations in one game and the shrinkage of the ‘safe zone’ forces them to gather together with a forest. Figure 1(a) shows the eliminating relations among all in the process of game. Combats usually happen between two teams teams in Table 1 with a forest. In the eliminating forest, the arrow We have noticed a Battle a team who happen to meet withthat, eachin other in the Royale map, andgame, knockout of can only be eliminated by another team or a ‘non-combat’ between any two nodes points towe the artificially winner in their combat, factor, which eliminating relation is a kind of unary or binary relation. When remove theand players happens then.means, Besides,the other factors can also cause knockout the dashed circle represents the node being knocked out for some condition when two teams eliminate each in other, we can denote all the eliminating relations in one game with a of players, such as ‘unsafe zone’ damage, car accident the game, non-combat reasons. For convenience, we shall call the tree with teammates’ connection to the server, relations etc. We callamong all teams in Table 1 with a forest. In the eliminating forest. damage, Figure loss 1(a)ofshows the eliminating the final winner to be the root by ‘central tree’ of the eliminating all the factorsthe other than between combat byany non-combat factors. A team forest, arrow two nodes points to isthe winner their combat, thetree’. dashed represents forest,inand other trees byand ‘side Root circle of every side tree is a eliminated frombeing the game if all members this team are knocked the node knocked out forinsome non-combat reasons.team Forknocked convenience, we shall call the tree with the final out for some non-combat reason. In Figure 1(a), the out. We say “team a eliminates team b” if the last player in team b tree with д is the central tree, tree’. and theRoot otheroftree withside root m winner to be the root by ‘central tree’ of the eliminating forest, androot other trees by ‘side every is knocked out by team a. The team who survives to the end is the is the side tree. tree a team out for some reason. In Figure 1(a), the tree with root � is the central tree, and winner of is this game. knocked The matching system andnon-combat scoring system in The forest-structured eliminating relations offer an inspiration �described other treeLeague with root is the side PUBGthe Professional can be as tree. follows: 1) there’re for new scoring mechanisms, where relative surviving time is con16 teams in each game, with 4 players per team; a team is defined to sidered. Since forest is not necessarily a connected graph and cannot be eliminated once all four members are knocked out; 2) knocking describe the relative relation within nodes in different trees, we out every player of another team is awarded 1 point, which is the shall reformulate the forest by adding a dashed arrow from every knockout point; 3) the teams are awarded rank points according to side tree root who ranks i th , to the node ranking (i − 1)th in the their rank in the reversed elimination sequence. The rank points reversed elimination sequence, thus transforming the forest to a are 10, 6, 5, 4, 3, 2, 1, 1 for the top eight teams, and 0 for the tree. The reformulated tree of the forest in Figure 1(a) is shown in last eight teams; 4) total score of a team is the sum of its knockout Figure 1(b), where team m is non-combat eliminated and ranks 10th points and rank points. in this game, thus attached to team l who ranks 9th in this game, As is shown above, the current scoring system regards every with a dashed arrow. In the reformulated tree, the directed edges knockout to be of identical value, and awards teams ranking above show two kinds of relations: 1) the relative surviving time relation in the reversed elimination sequence with scores. The reversed elim(eliminating relation) in solid arrow, which is prior to consider; ination sequence describes the chronological eliminating order of 2) the absolute surviving time relation in dashed arrow, which is teams. A team ranking i t h in reversed elimination sequence means secondary to consider. Based on the reformulated tree, we raise the that there are i −1 teams still alive when this team is eliminated, and ‘tree-based’ scoring mechanisms. Since the Battle Royale games

4 THE GRAPH-BASED MECHANISMS

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Table 2: The scores in the game shown in Table 1 using the current scoring system in PUBG Professional League, under the assumption that there’s only one player in each team. Team g i d b n e k a

Rank 1 2 3 4 5 6 7 8

Rank Point 10 6 5 4 3 2 1 1

Knockout Point 4 1 0 4 1 1 1 0

Total Score 14 7 5 8 4 3 2 1

Team l m c f j p o h

(a)

Rank 9 10 11 12 13 14 15 16

Rank Point 0 0 0 0 0 0 0 0

Knockout Point 1 1 0 0 0 0 0 0

Total Score 1 1 0 0 0 0 0 0

(b)

Figure 1: The eliminating forest and reformulated tree in the example in Table 1. encourage both knockout and survival, we still keep these two factors in our new mechanisms, and moreover keep their positive correlations with the total score. The conceptual rules are stated as follows:

relative order between every two teams in the reversed elimination sequence.

5 EXPERIMENTS 5.1 Experiment Design

• the knockout number is the Knockout Factor, which is the number of players knocked out by this team; • the location of this team in the reformulated tree determines its Value of Knockout (VoK); • total score of this team is the product of its Knockout Factor and VoK.

5.1.1 Scoring Systems Applied. We make a series of simulating experiments to show performance of tree-based mechanisms, comparing to the rank-based (RB) mechanism. We particularly apply the scoring system in PUBG Professional League stated before. Specifically, we apply two instances of layer-based mechanism with VoK calculating rules as, 1. Layer-based VoK in arithmetic progression (LB-ap): V oK = 1 + (L − l) × 0.5, and 2. Layer-based VoK in geometric progression (LB-gp): V oK = 1 × 1.5(L−l ) , where L is the longest distance between root and the other nodes, and l is the distance between the current node and root. As is shown, the VoK value of the layer farthest to the root is set to 1 under both scoring systems. The layer closer to the root has higher VoK value, and the root has the highest VoK value. The PageRank-on-tree (PR) scoring system we apply is to calculate the VoK value of each team with the classic PageRank algorithm, where damping parameter is set to be 0.85. Then we scale up all the VoK values to let the lowest equal to 1. We still use the example in Table 1 to elaborate LB-ap, LB-gp and PR in Table 3 We apply the scoring systems described above in the experiments, which are instances of RB, LB-ap, LB-gp and PR. To keep

The concept of VoK is intuitive: more reward should be given if the rival being knocked out is stronger. We shall give two classes of tree-based mechanisms, the main difference between whom is the way to calculate the VoK of each team. Define the distance between two nodes by the total number of edges on the shortest path between them in the reformulated tree. We say that two teams are in the same layer of the tree if they have identical distances to the root. Note that, the root of the reformulated tree represents the winner who is the unique team in the root layer. The first class of tree-based mechanism is called layer-based (LB) mechanism, where every team in the same layer of the reformulated tree has identical VoK value, and the layer closer to the root has higher VoK value. The second is called PageRank-on-tree (PR) mechanism, where the PageRank algorithm is used to calculate the VoK value of each team. Compared to the currently used rank-based mechanism who emphasizes on chronological order of elimination, the tree-based mechanisms care more about the

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Table 3: The VoKs of teams in the game shown in Table 1

Team g i d b n e k a

Layer 0 1 1 2 3 3 3 1

LB-ap 3.0 2.5 2.5 2.0 1.5 1.5 1.5 2.5

VoKs LB-gp 5.0625 3.375 3.375 2.25 1.5 1.5 1.5 3.375

PR 11.2041 6.5824 1.0 6.5657 1.85 1.85 1.85 1.0

Team l m c f j p o h

Layer 1 2 3 3 4 4 2 4

LB-ap 2.5 2.0 1.5 1.5 1.0 1.0 2.0 1.0

VoKs LB-gp 3.375 2.25 1.5 1.5 1.0 1.0 2.25 1.0

PR 3.4225 1.85 1.0 1.0 1.0 1.0 1.0 1.0

of any two teams a and b, we say that the order of a and b is reversed if a has higher skill level than b but gets lower score. Among 100 teams, there are P(100, 2) = 4950 pairs of order, in which the percentage of reversed order is ROR, indicating the ranking performance. Scoring systems are also used for incentivizing players. In Battle Royale games, players are encouraged to knock out as many rivals as possible and to survive to the end of game, which are interdependent targets, since a team can survive to the end if and only if she wins in every combat she participates. Moreover, strategically omitting combat is usually not welcomed by designers and audiences, thus we can take knockout as the main effort of teams to consider. SpK, the ration between total score and total knockout of a team, indicates the average reward for unit of effort (knocking a player out).

the comparability of results, we proportionally adjust the score of every team before analyzing, so that the total score awarded to all teams is equal among all the scoring systems. 5.1.2 Players’ Skill Level. We use the phrase ‘skill level’ to describe a player’s intrinsic ability of playing the game well. If a player has higher skill level than another, then she has a higher probability to win in the combat between them. The skill level of players forms a partially ordered set. Denote by s ≽ t if skill level s is not lower than skill level t. Then skill level has following properties: 1) reflexivity (s ≽ s); 2) antisymmetry (s ≽ t ∧ t ≽ s ⇒ s = t); 3) transitivity (s ≽ t ∧ t ≽ u ⇒ s ≽ u). Given the above properties, a one-toone function can be created between players’ skill level and real numbers, where we denote by q : Skill Level → Real Number , and ∀s, t ∈ Skill Level, qs ≥ qt ⇔ s ≽ t. With function q, we can denote any player i’s skill level si by a real number qsi directly, shorthand as qi . We further assume that, without loss of generality, the domain of q is [0, 1]. In the experiments, we restrict players’ initial skill level q to uniformly distribute on [0.200, 0.800]. A small change of skill level δ ∼ U [−0.005, 0.005] is introduced to the players who survive in a combat. This design is intended to simulate the fluctuation of the player’s state during a game. Note that, the initial skill level is a fixed property of every player, and the change of skill level in one game does not affect its initial skill level in the other games. Moreover, the fluctuation of the skill level is not allowed to violate the constraint 0 ≤ q ≤ 1.

5.2

Simulation Results

5.2.1 One-Player Team Mode. We first discuss a special setting where each team has only one player, knockout can only happen between two teams, and there must be one team winning and the other team losing in each combat. We shall call this setting by oneplayer team mode, and the simulation processes as Simulation 1 shows. One-player team mode also suits other occasions when a team lives or dies together and there is ignorable teammate damage or circumstance damage, such as when the game allows living players to resurrect their teammates easily.

5.1.3 Matching Scale. We organize simulating experiments under two conditions: one-player team mode and four-player team mode; then calculate scores under four scoring systems on the simulating results. Under each condition, we launch simulation of 100 teams, from which 16 teams are randomly selected in each game. First, we set a 1000-round simulation, where each team participates for around 160 times, to show the average performance of the scoring systems. Then we set a 100-round simulation, where each team participates for around 16 times, a scale of a regular match, to investigate performances of the scoring systems in the matches.

SIMULATION 1 : One Game of One-Player Team Mode initialize living teams’ set L := {all teams in this game}; while there is more than one team in L, do randomly choose two teams a and b from L; randomly selected a real number θ ∈ [0, 1]; if Skill_Level[a]/(Skill_Level[a] + Skill_Level[b]) > θ , then winner = a, loser = b; else winner = b, loser = a; record eliminating relation (winner, loser); remove loser from L; add a random real number δ ∼ U (−0.005, 0.005) to Skill_Level[winner ]; the unique remaining team in L is the winner.

5.1.4 Results Analysis. We analyze ranking performance and incentive of all four scoring systems with two main indicators: Reversed Order Rate (ROR) and Score per Knockout (SpK). Scoring systems are supposed to rank the teams in ‘right order’, where team with higher skill level gets higher score in the game. Given the skill level

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Table 4: The Reversed Order Rates in one-player team mode.

1000 rounds 100 rounds

RB 12.364% 21.818%

LB-ap 11.313% 20.101%

LB-gp 12.687% 21.980%

PR 11.596% 22.384%

(a) 1000-Round Simulation

(b) 100-Round Simulation Figure 2: Average Score per Knockout of One-Player Team Mode. In the simulation of one game of one-player team mode, the process randomly chooses two teams alive to hold a virtual combat. Each combat leads one team to be winner and the other to be loser, with the probability proportional to their skill level. The loser is eliminated and removed from the alive-team set, while the winner has a small fluctuation in its skill level. The process loops doing this job until the final team alive, who is the winner of this game, and records all the eliminating relations in the game. Note that, RB described earlier suits the occasion when there are four players in each team, thus under one-player team mode, rank scores used is a quarter of the original ones. Then we calculate scores of each team under four scoring systems. Table 4 statistically shows the ranking performances of four scoring systems by showing the RORs, which suggests that all four scoring systems have similar ranking performance. Figure 2(a) and (b) show the relation between average SpK and teams’ skill level in 1000-round and 100-round simulation respectively. The coordinate of each dot is the (skill level, average SpK) tuple of a team in the experiments. The straight line is the linear regression curve of the dots. The shadow beside the line shows the dispersion of the dots relative to the linear regression curve. Note that, the linear regression curve is used for indicating the variation tendency (increase or decrease), rather than claiming that the linear regression model can fit the experimental results. The experimental results indicate that, under both simulation scales, SpK value is negative correlated to skill level under RB scoring system, which means a tendency that teams with high skill level get less reward for each knockout than those with low skill

level. However, high-skill-level teams live longer and knock out more rivals in expectation, so the average skill level of their rivals should be higher. Therefore, a knockout of such a strong team should be worthy of higher value. However, RB scoring system achieves in the opposite way, which seems like a punishment on the teams with high skill level, unfair and discouraging for them. On the contrary, the other three scoring systems we raise in this research show a positive correlation between SpK and skill level, which shows more fairness and incentive for the high-skill-level teams. 5.2.2 Four-Player Team Mode. Now we discuss a setting identical to the Professional League of PUBG, called four-player team mode. Under this setting, each team has four players with synergy. Players in one team do not have to be knocked out in the same combat, and the other team who knocks out the last player in this team is defined as the one eliminating this team. The team survives to the end is the winner, even if there’s only one player remaining alive. Moreover, this setting contains the conditions that no knockout occurs in one combat, no one survives in one combat, and non-combat factor knockout, which do happen in a regular game. The process of four-player team mode is shown in Simulation 2. The process randomly chooses two alive teams to hold a virtual combat each time, until a unique team survives. The synergy of players in one team is shown as the sum of their skill level Q. A team with more alive players or stronger players has higher Q, and surviving chance of every player in this team increases in combats, and vice versa. If both teams are eliminated in one combat, we regard that one team is eliminated by the other, and the other is

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eliminated by a non-combat factor, so that the eliminating relations form a forest. After each combat, every player still alive may suffer a non-combat elimination with probability p = 0.001 if the winner has not been determined.

only about eliminating relations, elimination sequence and knockout numbers, which also monotonously related to skill level, the distortions of the probabilities will not affect RORs and the order of VoKs among all teams, thus not influencing our analysis. According to the experimental results, we notice that, under fourplayer team mode: 1) four scoring systems have similar ranking performance in the long run, but their ranking performances vary a little in the short run (in Table 5), where LB-ap and RB outperform a little than the other two; 2) all scoring systems show incentive for high-skill-level teams, but the degree is gradually increasing in the order of RB, LB-ap, LB-gp and PR (in Figure 3). Specifically, the horizontal axes in Figure 3 represent the average initial skill level of the players in each team, a quarter of sum skill level of the teams, thus mainly distributing on [0.300, 0.700].

SIMULATION 2 : One Game of Four-Player Team Mode initialize living teams’ set L := {all teams in this game}, living players’ dict P := {teamID: {playerID} for all players in this team} for all teams in this game; while there is more than one team in L, do randomly choose two teams a and b from L; calculate Q a := sum of skill level of players alive in team a, Qb := sum of skill level of players alive in team b; for each player i in team a and b, do x := teamID of i’s team, y:= teamID of the other team; randomly select a real number θ ∈ [0, 1]; if Skill_Level[i] × Q x /Qy > θ , then /* i survives in this combat */ add a random real number δ ∼ U (−0.005, 0.005) to Skill_Level[i]; else /* i is knocked out in this combat */ delete i from P[x]; record one more knockout of team y; if one team is eliminated and the other is not in the combat between a and b, then w := the team surviving in this combat, l := the team eliminated in this combat; remove l from L; record eliminating relation (w, l) else if both teams are eliminated, then remove a and b from L; randomly selected a real number θ ∈ [0, 1]; if Q a /(Q a + Qb ) > θ , then w := a, l := b; else w := b, l := a; record eliminating relation (w, l); if L is empty, then w is the winner and process finishes; else regard w as non-combat eliminated; every player alive is non-combat knocked out with a probability p = 0.001; for every team j in L: /* to verify whether each team is non-combat eliminated or not */ if no player alive in j: remove j from L; if only one team in L, then the unique team remaining is the winner and process finishes; the unique team in L is the winner.

5.2.3 Experiment Summary. Our experiments show, RB performs poorly in incentivizing high-skill-level teams and offering fair scores to indicate their skill level. The other three we raise in this research can make up for this shortcoming. However, though LB-gp and PR have significant incentive and fairness for the high-skilllevel teams, the scores disperse a lot, and cannot be used for evaluating skill level of the teams and players. LB-ap has more incentive than RB, and the scores under LB-ap have smaller dispersion than that under RB, both smaller than LB-gp and PR. This indicates that, besides achieving incentive and fairness, LB-ap can also be used for evaluating skill levels of the teams with the scoring results.

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CONCLUSION

In this research, we raise three new scoring mechanisms for Battle Royale games, and carry out simulating experiments to make comparison among four scoring mechanisms, including the currently used one. The experimental results show, the currently used scoring system performs poorly in incentivizing and offering fair scores for high-skill-level teams, and among all the mechanisms, LB-ap shows more desirable properties than the other three. Future works can be on the influence of the parameters chosen, such as the ranking scores in RB, the tolerance in LB-ap and common ration in LB-gp, on the properties of mechanisms.

REFERENCES [1] Wang, H. and Sun, C. T. 2011. Game reward systems: Gaming experiences and social meanings. In DiGRA conference (Vol. 114). https://citeseerx.ist.psu.edu/ viewdoc/download?doi=10.1.1.221.4931&rep=rep1&type=pdf [2] Shneiderman, B., Plaisant, C., Cohen, M. S., Jacobs, S., Elmqvist, N., and Diakopoulos, N. 2016. Designing the user interface: strategies for effective human-computer interaction. Pearson. [3] Lee, C.-I, Chen, I-P., Hsieh, C.-M., and Liao, C.-N. 2017. Design Aspects of Scoring Systems in Game. Art and Design Review, 5, 26-43. https://doi.org/10.4236/adr. 2017.51003 [4] Crawford, C. 1984. The art of computer game design. http://www.stonetronix. com/gamedesign/art_of_computer_game_design.pdf [5] Choi, G., and Kim, M. 2018. Battle Royale game: In search of a new game genre. International Journal of Culture Technology (IJCT), 2(2), 5. https://core.ac.uk/ download/pdf/162021462.pdf#page=6 [6] Rosenbusch, H., Röttger, J., and Rosenbusch, D. 2020. Would Chuck Norris certainly win the Hunger Games? Simulating the result reliability of Battle Royale games through agent-based models. Simulation & Gaming, 51(4), 461-476. https://doi.org/10.1177/1046878120914336 [7] Takami, K., Taguchi, M., & Giffen, K. 2003. Battle royale. Tokyopop. [8] Dawkins, K. 2000. Battle royale of the 21st century. Seedling, 17(1), 2-8. [9] Rahkar Farshi, T. 2020. Battle royale optimization algorithm. Neural Computing and Applications, 1-19. https://doi.org/10.1007/s00521-020-05004-4

As we can see, Simulation 2 contains most of the cases in a real PUBG game. Though the probability of every event may not be consistent with a real game, it keeps the monotonicity between winning probability and skill level. As the scoring systems care

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Table 5: The Reversed Order Rates in four-player team mode.

1000 rounds 100 rounds

RB 4.303% 11.232%

LB-ap 4.222% 10.424%

LB-gp 4.545% 12.646%

PR 4.798% 13.879%

(a) 1000-Round Simulation

(b) 100-Round Simulation Figure 3: Average Score per Knockout of Four-Player Team Mode. [13] Page, L., Brin, S., Motwani, R., & Winograd, T. 1999. The PageRank citation ranking: Bringing order to the web. Stanford InfoLab. http://ilpubs.stanford.edu: 8090/422/ [14] Koschützki D., Lehmann K.A., Peeters L., Richter S., Tenfelde-Podehl D. and Zlotowski O. 2005. Centrality Indices. In: Brandes U., Erlebach T. (eds) Network Analysis. Lecture Notes in Computer Science, vol 3418. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31955-9_3 [15] Gleich, D. F. (2015). PageRank beyond the Web. SIAM REVIEW, 57(3), 321-363. https://doi.org/10.1137/140976649

[10] Lames, M. and McGarry, T. 2007. On the search for reliable performance indicators in game sports. International Journal of Performance Analysis in Sport, 7(1), 62-79. https://doi.org/10.1080/24748668.2007.11868388 [11] McGarry, T. 2009. Applied and theoretical perspectives of performance analysis in sport: Scientific issues and challenges. International Journal of Performance Analysis in Sport, 9:1, 128-140, https://doi.org/10.1080/24748668.2009.11868469 [12] Brin, S. and Page, L. 1998. The anatomy of a large-scale hypertextual web search engine. Computer networks and ISDN systems, 30(1-7), 107-117. https://doi.org/ 10.1016/S0169-7552(98)00110-X

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