Computing Constrained Approximate Equilibria in Polymatrix Games

Argyrios Deligkas, John Fearnley, Rahul Savani

Abstract: This paper studies constrained approximate Nash equilibria in polymatrix games. We show that is $$\mathtt {NP}$$-hard to decide if a polymatrix game has a constrained approximate equilibrium for 9 natural constraints and any non-trivial $$\epsilon $$. We then provide a QPTAS for polymatrix games with bounded treewidth and logarithmically many actions per player that finds constrained approximate equilibria for a wide family of constraints.