Approximate Well-Supported Nash Equilibria Below Two-Thirds

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