Mafia/Warewolf Party Game

A Mafia/Warewolf Party Game is a party game that ...

• See: Information Asymmetry, Strategy Game, Social Skills, Roleplay, Homo Economicus, Nash Equilibrium, Mixed Strategy.

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References

2017

• (Wikipedia, 2017) ⇒ https://en.wikipedia.org/wiki/Mafia_(party_game) Retrieved:2017-5-31.
  • Mafia, also known as Werewolf, is a party game created by Dmitry Davidoff in 1986 modelling a conflict between an informed minority, the mafia, and an uninformed majority, the innocents. At the start of the game, each player is secretly assigned a role affiliated with one of these teams. The game has two alternating phases: night, during which the mafia may covertly "murder" an innocent, and day, in which surviving players debate the identities of the mafia and vote to eliminate a suspect. Play continues until all of the mafia have been eliminated or until the mafia outnumbers the innocents.

2017

• (Wikipedia, 2017) ⇒ https://en.wikipedia.org/wiki/Mafia_(party_game)#Game_theory Retrieved:2017-5-31.
  • Mafia is a complicated game to model, so most analyses of optimal play have assumed both (a) that there are only townsfolk and mafiosi and (b) that the townsfolk never have a probability of identifying the Mafia that is better than chance. Early treatment of the game concentrated on simulation, while more recent studies have tried to derive closed-form equilibrium solutions for perfect play. In 2006, the computer scientists Braverman, Etesami and Mossel proved that without detectives and with perfect players the randomized strategy is optimal for both citizens and mafia. When there is a large enough number of players to give both groups similar probability of winning, they showed that the initial number of mafiosi m needs to be proportional to the square root of the total number of players P, that is [math]\displaystyle{ {\textstyle m \propto \sqrt{P}} }[/math] . With a simulation, they confirmed that 50 mafiosi would have almost a 50% chance to win among 10,000. The Mafia's chance of victory is [math]\displaystyle{ W(m, P) \approx \frac{m}{\sqrt{P}}, }[/math] which is a good approximation when the right hand side is below 40%. If any detectives are added to the game, Braverman et al. proved that the number of mafiosi must remain at a fixed proportion of the total number of players for their chance of winning to remain constant. In 2008, Erlin Yao derived specific analytical bounds for the mafia's win probability when there are no detectives. In a paper from 2010, exact formula for the probability that the mafia wins was found. Moreover, it was shown that the parity of the initial number of players plays an important role. In particular, when the number of mafiosi is fixed and an odd player is added to the game (and ties are resolved by coin flips), the mafia-winning chance do not drop but rise by a factor of approx. [math]\displaystyle{ \sqrt{\pi/2} }[/math] (equality in the limit of the infinite number of players).

2014

• (Girlea et al., 2014) ⇒ Codruta Girlea, Eyal Amir, and Roxana Girju. (2014). “Tracking Beliefs and Intentions in the Werewolf Game.” In: Proceedings of the Fourteenth International Conference on Principles of Knowledge Representation and Reasoning. ISBN:1-57735-657-8, 978-1-57735-657-8
  • QUOTE: An example of such a domain is the Werewolf game. Here, players are assigned the roles of either villagers or werewolves. The game proceeds in alternating day and night stages, overlooked by an impartial judge. By night, unseen by villagers, the werewolves choose and kill a victim. The victim’s identity is announced by the judge at the beginning of the next day. Then, the rest of the villagers discuss and vote to execute one person who they agree is a werewolf. The problem is to predict the outcome of each player’s vote.

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