A Polynomial-Time Algorithm for 1/3-Approximate Nash Equilibria in Bimatrix Games

Since the celebrated PPAD-completeness result for Nash equilibria in bimatrix games, a long line of research has focused on polynomial-time algorithms that compute ε-approximate equilibria. Finding best possible approximation guarantee we can have polynomial time been fundamental and non-trivial pursuit settling complexity approximate Despite significant amount effort, algorithm Tsaknakis Spirakis [38], with an (0.3393 + δ ), remains state art over last 15 years. In this paper, propose new refinement Tsaknakis-Spirakis algorithm, resulting computes \((\frac{1}{3}+\delta) \) -Nash equilibrium, any constant > 0. The main idea our approach is to go beyond use convex combinations primal dual strategies, as defined optimization framework enrich pool strategies from which build strategy profiles output certain bottleneck cases algorithm.