Computing Equilibrium beyond Unilateral Deviation

Mingyang Liu, Gabriele Farina, Asuman E. Ozdaglar

Keywords: Strong Equilibrium, Complexity, No-regret Learning

TL;DR: Fixed parameter lower bounds of strong equilibrium and algorithm that matches the lower bound

Abstract: 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.

Primary Area: learning theory

Submission Number: 15027