Algorithms and Complexity for Computing Nash Equilibria in Adversarial Team Games

Ioannis Anagnostides, Fivos Kalogiannis, Ioannis Panageas, Emmanouil-Vasileios Vlatakis-Gkaragkounis, Stephen McAleer

Abstract: Adversarial team games model multiplayer strategic interactions in which a team of identically-interested players is competing against an adversarial player in a zero-sum game. Such games capture many well-studied settings in algorithmic game theory, unifying two-player zero-sum games and potential games, but go well-beyond to environments wherein the cooperation of one team---in the absence of explicit communication---is obstructed by competing entities; the latter setting remains poorly understood despite its numerous applications, and serves as an important step towards understanding more realistic strategic interactions that feature both competing and shared interests. Since the seminal work of Von Stengel and Koller (GEB '97), different solution concepts have received attention from an algorithmic standpoint. Yet, the complexity of the standard Nash equilibrium has remained open.