In this paper, we study the class of games known as hidden-role games in which players get privately assigned a team 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 real-world security settings, where a distributed system wants to operate while some of its nodes are controlled by adversaries. There has been little to no formal mathematical grounding of such settings in the literature, and it is not even immediately clear what the right solution concept is. In particular, the suitable notion of equilibrium depends on communication available to the players (whether players can communicate, whether they can communicate in private, and whether they can observe who is communicating), and defining it turns out to be a nontrivial task with several surprising consequences. We show that in certain cases, including the above recreational games, near-optimal equilibria can be computed efficiently. In most other cases, we show that computing an optimal equilibrium is either NP-hard or coNP-hard. Lastly, we experimentally validate our approach by computing nearly-exact equilibria for complete Avalon instances up to 6 players whose size in terms of number of information sets is larger than $10^{56}$.

翻译：本文研究被称为隐藏角色博弈的一类博弈，其中玩家被私下分配归属队伍，并面临识别并与队友合作的挑战。该模型既包括流行娱乐游戏（如《黑手党/狼人》系列和《抵抗组织：阿瓦隆》），也包括现实世界中的安全场景（如分布式系统在部分节点被对手控制的情况下需保持运行）。现有文献中缺乏对这些场景的严格数学基础，甚至其合适的解概念也尚未明确。具体而言，均衡的恰当定义取决于玩家可用的通信方式（能否通信、能否私密通信、能否观察通信行为），而定义该概念是一项具有若干意外结论的非平凡任务。我们证明，在某些情况下（包括上述娱乐游戏），接近最优的均衡可被高效计算；而在大多数其他情况下，计算最优均衡要么是NP难的，要么是coNP难的。最后，我们通过实验验证了该方法：为完整阿瓦隆实例（最多6名玩家，其信息集规模超过$10^{56}$）计算了近似的精确均衡。