标题： 狼人杀游戏中的最优策略：理论研究 显示英文标题

标题： Optimal Strategy in the Werewolf Game: A Theoretical Study

摘要： 在本文中，我们从博弈论的角度研究了狼人杀游戏——一种广泛进行的战略社会推理游戏，涉及两个对立派系的最优策略。 我们考虑两种情景：没有先知的游戏中和有先知的游戏中。 在没有先知的情景中，我们提出了一种增强策略，称为“随机策略+”，该策略显著提高了狼人组相对于传统随机策略的获胜概率。 在有先知的情景中，我们将游戏重新建模为一个特定约束下的扩展形式贝叶斯博弈，并推导出先知的最优策略，该策略导致了一个完美贝叶斯均衡（PBE）。 本研究为建模狼人杀游戏提供了一个严格的分析框架，并对在不对称和不完全信息下战略决策制定提供了更广泛的见解。 显示英文摘要

摘要： In this paper, we investigate the optimal strategies in the Werewolf Game-a widely played strategic social deduction game involving two opposing factions-from a game-theoretic perspective. We consider two scenarios: the game without a prophet and the game with a prophet. In the scenario without a prophet, we propose an enhanced strategy called ``random strategy+'' that significantly improves the werewolf group's winning probability over conventional random strategies. In the scenario with a prophet, we reformulate the game as an extensive-form Bayesian game under a specific constraint, and derive the prophet's optimal strategy that induces a Perfect Bayesian Equilibrium (PBE). This study provides a rigorous analytical framework for modeling the Werewolf Game and offers broader insights into strategic decision-making under asymmetric and incomplete information.