Optimal Strategy in the Werewolf Game: A Theoretical Study

TL;DR

This paper analyzes optimal strategies in the Werewolf Game using game theory, introducing a new strategy for the werewolf side and deriving the prophet's optimal strategy under Bayesian equilibrium, advancing understanding of strategic decision-making.

Contribution

It introduces the 'random strategy+' for werewolves and formulates the game as a Bayesian model to find the prophet's optimal strategy, providing a rigorous analytical framework.

Findings

'random strategy+' improves werewolf win probability

Prophet's optimal strategy induces PBE in Bayesian game

Framework models strategic decisions under asymmetric info

Abstract

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.