The Dynamics of Minority versus Majority Behaviors: A Case Study of the Mafia Game
Abstract
:1. Introduction
2. Related Works
2.1. The Mafia Game
- Judge: The judge has to guide the course of the game, and not participate with any team. The game begins at night. Firstly, everyone needs to close their eyes, except for the judge and the Mafias. The judge will let the Mafias know who the teammates are and identify the player they want to kill. Then, let the Mafias close their eyes, tell the Sheriffs to open eyes to realize teammates, and verify players. During the daytime, the judge tells everyone to open their eyes and declare the player dead based on the results of the Mafia killings at night. After this, players will be directed to speak in order and point out the players they suspect of being a Mafia by the judge. Finally, the player is instructed to vote, noting that the player with the most votes will be declared out of the referendum by the judge. After the progress above, the judge will conduct the second night.
- Mafias: The Mafias’ goal is to kill all the players of the Citizen camp. Hence, they will disguise themselves as much as possible and mislead other players during the daytime. On the first night, guided by the judge, they identify their teammates and use hand signals to tell the judge which player they want to kill. In offline game conditions, the Mafias communicate by using gestures that do not make a sound. In the online game, voice communication is possible. On the first night, they make a random choice of players to kill. On the subsequent nights, they choose the player most likely to know their identity to kill (Sheriffs or Citizens), depending on the daytime situation, to ensure victory for the Mafias. Since the simple version of the Mafia game does not have a role that prevents players from being killed, the Mafias will succeed in killing players.
- Citizens: The Citizens’ goal is to help the Sheriff to win the game for the Citizen camp. The Citizens will close their eyes at night without any extra information. During the daytime, they will be guided by the judge to speak by pointing out the players they suspect of being Mafias. They vote to lynch the players they think are Mafias based on their analysis of the game situation. They vote by telling the judge the player number. All players will participate in the voting.
- Sheriffs: The Sheriffs’ goal is the same as the Citizen’s. During the night, they will verify the true identity of other players, guided by a judge. During the daytime, they will inform other players of their verification results when they are speaking. They will convince other players of their identity as much as possible, to guide other players to vote the Mafias out of the game.
2.2. Research Development on Mafia Game
3. Assessment Methodology
3.1. Game Progress Model and Game Refinement Theory
3.2. Game-Refinement Theory in the Mafia Game
- Judge: Hosts the game, not participating with any team.
- Mafias: Kills one character (except the Mafia) every night and pretends to be a player during the daytime.
- Citizens: Votes to lynch someone during the daytime.
- Sheriffs: Each night, the Sheriff can discover the real identity of a player (except the Sheriff).
- Mafias: Let be the sum of the and , where indicates the average number of killing actions at night, and indicates the number of players who are lynched by voting with Mafias during the daytime.
- Citizens: Let be the average number of Mafias who are lynched by Citizen voting.
- Sheriffs: Let be the average number of Mafias with their identity confirmed by the Sheriffs and then be lynched by voting.
3.3. Motion in Mind Model
4. Experiment Results and Its Analysis
4.1. Simulation Setup and Analysis
- Sheriff (S): Generally, after the Sheriffs discovered that a player’s identity is “Mafia”, there is a high probability that they will vote for the player in the next voting, and induce other Citizens to vote for this player. Therefore, we set a parameter to indicate the possibility of exposing the identity of Mafias.
- Mafia (M): The Mafias kill the Citizens randomly except that one of them has been exposed by any sheriff. At this time, the Sheriff that revealed them would be their target.
- Citizen (C): Because all the Citizens do not know the identity of each player, there is no guarantee that all Citizens will believe the Sheriff’s speech. Therefore, we set a parameter for each Citizen to indicate that possibility of believing in the Sheriff.
Algorithm 1: Mafia simulation |
4.2. Results Analysis of
4.3. Result Analysis of
5. Discussion
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Game | |||
---|---|---|---|
Chess [2,26] | 35 | 80 | 0.074 |
Go [26] | 250 | 208 | 0.076 |
Basketball [12] | 36.38 | 82.01 | 0.073 |
Soccer [12] | 2.64 | 22 | 0.073 |
Badminton [12] | 46.34 | 79.34 | 0.086 |
Dota 6.80 [25] | 68.6 | 106.2 | 0.078 |
2,4,2 | 2275 | 7725 | 0.3439 | 0.2134 | 0.2946 | 0.146 |
2,8,3 | 825 | 9175 | 0.2613 | 0.092 | 0.1913 | 0.0518 |
2,10,2 | 2901 | 7099 | 0.2296 | 0.0722 | 0.1997 | 0.0423 |
2,10,5 | 125 | 9875 | 0.2503 | 0.0621 | 0.1257 | 0.0357 |
2,14,2 | 5871 | 4129 | 0.1966 | 0.0459 | 0.1804 | 0.0288 |
5,10,5 | 2170 | 7830 | 0.1145 | 0.0550 | 0.1058 | 0.0035 |
4,15,2 | 7059 | 2941 | 0.1235 | 0.0394 | 0.1683 | 0.0135 |
7,15,7 | 2138 | 7862 | 0.071 | 0.0318 | 0.0674 | 0.0015 |
9,15,10 | 365 | 9635 | 0.0571 | 0.0301 | 0.0453 | 0.0024 |
10,15,10 | 630 | 9370 | 0.0506 | 0.0302 | 0.0444 | 0.0026 |
2,4,2 | 2275 | 7725 | 0.190 | 0.035 | 0.635 | 0.097 |
4,4,2 | 5257 | 4743 | 0.243 | 0.078 | 0.323 | 0.016 |
2,8,3 | 825 | 9175 | 0.053 | 0.004 | 0.473 | 0.067 |
2,10,2 | 2901 | 7099 | 0.180 | 0.014 | 0.529 | 0.069 |
2,10,5 | 125 | 9875 | 0.009 | 0.0003 | 0.258 | 0.021 |
2,12,6 | 12 | 9988 | 0.0006 | 2.279 | 0.178 | 0.010 |
5,10,5 | 2170 | 7830 | 0.067 | 0.008 | 0.214 | 0.011 |
4,15,2 | 7059 | 2941 | 0.225 | 0.015 | 0.181 | 0.012 |
4,15,4 | 3286 | 6714 | 0.110 | 0.007 | 0.214 | 0.011 |
7,15,7 | 2138 | 7862 | 0.038 | 0.004 | 0.122 | 0.003 |
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Ri, H.; Kang, X.; Khalid, M.N.A.; Iida, H. The Dynamics of Minority versus Majority Behaviors: A Case Study of the Mafia Game. Information 2022, 13, 134. https://doi.org/10.3390/info13030134
Ri H, Kang X, Khalid MNA, Iida H. The Dynamics of Minority versus Majority Behaviors: A Case Study of the Mafia Game. Information. 2022; 13(3):134. https://doi.org/10.3390/info13030134
Chicago/Turabian StyleRi, Hong, Xiaohan Kang, Mohd Nor Akmal Khalid, and Hiroyuki Iida. 2022. "The Dynamics of Minority versus Majority Behaviors: A Case Study of the Mafia Game" Information 13, no. 3: 134. https://doi.org/10.3390/info13030134