Computing Equilibrium beyond Unilateral Deviation

Most familiar equilibrium concepts, such as Nash and correlated equilibrium, guarantee only that no single player can improve their utility by deviating unilaterally. They offer no guarantees against profitable coordinated deviations by coalitions. Although the literature proposes notions to address multilateral deviations (\emph{e.g.}, strong Nash and coalition-proof equilibrium), these generally fail to exist. In this paper, we study a solution concept that accommodates multi-player deviations and is guaranteed to exist. We prove a fixed-parameter lower bound on the complexity of computing such an equilibrium and present an algorithm that matches this bound.