标题： 狼人杀中的最优策略：一种博弈论视角 显示英文标题

标题： Optimal Strategy in Werewolf Game: A Game Theoretic Perspective

摘要： 狼人杀游戏，也称为黑手党游戏，是一种社会推理游戏，它模拟了知情的少数群体（狼人组）与不知情的多数群体（平民组）之间的冲突。 本文从博弈论的角度探讨狼人杀游戏的最优策略，重点研究存在先知和不存在先知的情况。 首先我们考察了没有先知情况下的现有策略，并提出了“随机策略+”，该策略为狼人组提供了更高的获胜概率。 然后我们进一步研究了存在先知的情况，并发现，在特定规则下，存在先知的游戏中可以转化为一个具有完全但不完美信息的扩展博弈。 我们构建了一个模型并设计了一个算法以实现PBE，并最大化平民组的获胜概率。 最后，我们研究了在没有任何限制条件下的PBE的一个性质。 显示英文摘要

摘要： 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 explores the optimal strategies of the werewolf game from the perspective of game theory, focusing on cases both with and without prophet. First we examine the existing strategy in game without prophet and propose ``random strategy +", which provides an improved winning probability for the werewolve group. Then we further study the game with prophet, and find the game with prophet can be transformed into a 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 citizen group's winning probability. In the end, we examine a property of PBE in game without any restriction.