In this paper, we study the class of games known as hidden-role games in which players are assigned privately to teams and are faced with the challenge of recognizing and cooperating with teammates. This model includes both popular recreational games such as the Mafia/Werewolf family and The Resistance (Avalon) and many real-world settings, such as distributed systems where nodes need to work together to accomplish a goal in the face of possible corruptions. There has been little to no formal mathematical grounding of such settings in the literature, and it was previously not even clear what the right solution concepts (notions of equilibria) should be. A suitable notion of equilibrium should take into account the communication channels available to the players (e.g., can they communicate? Can they communicate in private?). Defining such suitable notions turns out to be a nontrivial task with several surprising consequences. In this paper, we provide the first rigorous definition of equilibrium for hidden-role games, which overcomes serious limitations of other solution concepts not designed for hidden-role games. We then show that in certain cases, including the above recreational games, optimal equilibria can be computed efficiently. In most other cases, we show that computing an optimal equilibrium is at least NP-hard or coNP-hard. Lastly, we experimentally validate our approach by computing exact equilibria for complete 5- and 6-player Avalon instances whose size in terms of number of information sets is larger than $10^{56}$.

翻译：本文研究一类被称为隐藏角色博弈的博弈形式，其中玩家被私下分配到不同团队，面临识别并与队友合作的挑战。该模型既包括狼人杀/米勒山谷狼人家族和《抵抗组织》（阿瓦隆）等流行娱乐游戏，也涵盖诸多现实场景，例如在可能发生节点腐败的情况下需要协同完成目标的分布式系统。现有文献对此类场景缺乏正式的数学基础，甚至连合适的解概念（均衡概念）都尚未明确。合理的均衡概念需考虑玩家可用的通信渠道（例如能否通信？能否私下通信？）。定义此类恰当概念是一项具有多项意外结论的非平凡任务。本文首次为隐藏角色博弈提供了严格的均衡定义，克服了其他非专为隐藏角色博弈设计的解概念存在的严重局限性。我们进一步证明，在某些情形下（包括上述娱乐游戏），最优均衡可被高效计算。而在绝大多数其他情形中，计算最优均衡至少是NP-困难或coNP-困难的。最后，我们通过计算完整的5人及6人阿瓦隆游戏实例（其信息集数量规模超过10^56）的精确均衡，实验验证了所提方法的有效性。