Optimal Strategy in the Werewolf Game: A Theoretical Study

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.