English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this paper, we study a game called ``Mafia,'' in which different playershave different types of information, communication and functionality. Theplayers communicate and function in a way that resembles some real-lifesituations. We consider two types of operations. First, there are operationsthat follow an open democratic discussion. Second, some subgroups of playerswho may have different interests make decisions based on their own groupinterest. A key ingredient here is that the identity of each subgroup is knownonly to the members of that group. In this paper, we are interested in the beststrategies for the different groups in such scenarios and in evaluating theirrelative power. The main focus of the paper is the question: How large andstrong should a subgroup be in order to dominate the game? The concrete modelstudied here is based on the popular game ``Mafia.'' In this game, there arethree groups of players: Mafia, detectives and ordinary citizens. Initially,each player is given only his/her own identity, except the mafia, who are giventhe identities of all mafia members. At each ``open'' round, a vote is made todetermine which player to eliminate. Additionally, there are collectivedecisions made by the mafia where they decide to eliminate a citizen. Finally,each detective accumulates data on the mafia/citizen status of players. Thecitizens win if they eliminate all mafia members. Otherwise, the mafia wins. Wefirst find a randomized strategy that is optimal in the absence of detectives.This leads to a stochastic asymptotic analysis where it is shown that the twogroups have comparable probabilities of winning exactly when the totalpopulation size is $R$ and the mafia size is of order $\sqrt{R}$. We then showthat even a single detective changes the qualitative behavior of the gamedramatically. Here, the mafia and citizens have comparable winningprobabilities only for a mafia size linear in $R$. Finally, we provide asummary of simulations complementing the theoretical results obtained in thepaper.

Mafia: A theoretical study of players and coalitions in a partial information environment