Small Support Equilibria in Large Games

TL;DR

This paper presents a simplified proof for the existence of small support approximate Nash equilibria in large games, improving bounds and extending results to n-player and graphical games.

Contribution

It offers a new, simpler proof that enhances bounds on support size and generalizes small probability game results to n-player and graphical games.

Findings

Improved support size bounds for approximate Nash equilibria in n-player games.

Extended small probability game results from two-player to n-player games.

Established logarithmic support bounds in graphical 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.