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Efficiently computing Nash Equilibria (NEs) for multiplayer games is still an open challenge in computational game theory. In fact, it is not only hard to compute NEs in multiplayer games, but also hard for players independently choosing strategies and then forming an NE because NEs are not exchangeable. This thesis focuses on computing Team-Maxmin Equilibria (TMEs), which was introduced as a solution concept for zerosum multiplayer games where players in a team having the same utility function play against an adversary. The Correlated TME (CTME) is a variant of the TME, where team players can synchronize (correlate) their strategies by exploiting a mediator recommending actions to them through communication. According to different forms of communication, the CTME in extensive-form games includes: 1) the TME with Coordination device (TMECor) for the situation where team players can communicate their actions only before the play of the game; and 2) the TME with Communication device (TMECom) for the situation where team players can communicate their actions before the play of the game and during the game’s execution. The TME has some fascinating properties, e.g., it is unique in general, which can avoid the equilibrium selection problem. Moreover, TMEs can capture many realistic scenarios, including: 1) a team of players play against a target player in poker games; and 2) multiple defense resources schedule and patrol against the adversary in security games. Unfortunately, existing algorithms are inefficient to compute TMEs in large games. Therefore, in this thesis, we develop efficient algorithms to compute TMEs in normal-form and extensive-form games, including general algorithms and domain-specific algorithms for applications. First, we develop a novel incremental strategy generation algorithm to compute TMEs in normal-form games efficiently, which is the first incremental strategy generation algorithm guaranteeing to converge to a TME. Second, we apply the TME to a novel

Computing team-maxmin equilibria in zero-sum multiplayer games