Approximate Well-supported Nash Equilibria Below Two-thirds

Abstract

In an $$\epsilon $$∈-Nash equilibrium, a player can gain at most $$\epsilon $$∈ by changing his behaviour. Recent work has addressed the question of how best to compute $$\epsilon $$∈-Nash equilibria, and for what values of $$\epsilon $$∈ a polynomial-time algorithm exists. An $$\epsilon $$∈-well-supported Nash equilibrium ($$\epsilon $$∈-WSNE) has the additional requirement that any strategy that is used with non-zero probability by a player must have payoff at most $$\epsilon $$∈ less than a best response. A recent algorithm of Kontogiannis and Spirakis shows how to compute a 2/3-WSNE in polynomial time, for bimatrix games. Here we introduce a new technique that leads to an improvement to the worst-case approximation guarantee.