Approximate Well-supported Nash Equilibria Below Two-thirds

In an ϵ-Nash equilibrium, a player can gain at most ϵ by changing his behaviour. Recent work has addressed the question of how best to compute ϵ-Nash equilibria, and for what values of ϵ a polynomial-time algorithm exists. An ϵ-well-supported Nash equilibrium (ϵ-WSNE) has the additional requirement that any strategy that is used with non-zero probability by a player must have payoff at most ϵ 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