Optimal strategy in the werewolf game: a game-theoretic perspective

arXiv:2408.17177v1 Announcement Type: new Abstract: Werewolf game, also known as mafia game, is a social deduction game that models the conflict between an informed minority (werewolf group) and an uninformed majority (citizen group). This paper investigates the optimal strategies of the werewolf game from the perspective of game theory, focusing on cases with and without prophet. First, we investigate the existing strategy in the game without prophet and propose “random strategy +”, which provides an improved winning probability for the werewolf group. Then, we further study the game with prophet and find that the game with prophet can be transformed into an extensive game with complete but imperfect information under a specific rule. We construct a model and design an algorithm to achieve PBE and maximize the winning probability of the citizen group. Finally, we investigate a property of PBE in the game without any restriction.