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游戏，其中玩家被秘密分配至不同团队，并面临识别队友并与之合作的挑战。该模型既包含流行的娱乐游戏（如狼人杀系列游戏与《抵抗组织：阿瓦隆》），也涵盖许多现实场景，例如分布式系统中各节点需要在可能存在恶意节点的情况下协同完成目标。现有文献对此类场景缺乏严格的数学基础，甚至此前连合适的解概念（均衡概念）都尚未明确。合适的均衡概念应当考虑玩家可用的通信渠道（例如：能否通信？能否私下通信？）。定义此类合适的概念被证明是一项具有多重意外影响的非平凡任务。本文首次为隐藏角色博弈提出了严格的均衡定义，该定义克服了其他非针对隐藏角色博弈设计的解概念的严重局限。我们进而证明，在特定情形下（包括上述娱乐游戏），最优均衡可以被高效计算。在大多数其他情形中，我们证明计算最优均衡至少是NP难或coNP难的。最后，我们通过为完整5人和6人阿瓦隆实例计算精确均衡进行实验验证，这些实例的信息集数量规模超过$10^{56}$。