Small Support Equilibria in Large Games

Abstract: In this note we provide a new proof for the results of Lipton et al. on the existence of an approximate Nash equilibrium with logarithmic support size. Besides its simplicity, the new proof leads to the following contributions: 1. For n-player games, we improve the bound on the size of the support of an approximate Nash equilibrium. 2. We generalize the result of Daskalakis and Papadimitriou on small probability games from the two-player case to the general n-player case. 3. We provide a logarithmic bound on the size of the support of an approximate Nash equilibrium in the case of graphical games.