Hidden-Role Games: Equilibrium Concepts and Computation

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 $10^{56}$.