Small Support Equilibria in Large Games

In this note we provide a new proof for the results of Lipton et al. [3] 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 [4] 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. Center for the Mathematics of Information, Department of Computing and Mathematical Sciences, California Institute of Technology. e-mail:[email protected]. The author wishes to thank Constantinos Daskalakis and Siddarth Barman for useful discussions and comments. The author gratefully acknowledges support from a Walter S. Baer and Jeri Weiss fellowship.