Computing Equilibria in Anonymous Games

TL;DR

This paper introduces efficient algorithms for approximating Nash equilibria in large anonymous games with few strategies, providing polynomial-time solutions and a PTAS for epsilon-equilibria.

Contribution

It presents the first polynomial-time algorithms for approximate pure Nash equilibria in anonymous games with many players and few strategies.

Findings

Existence of approximate pure Nash equilibria in polynomial time

Approximation bound of O(s^2 L) for the equilibria

A PTAS for finding epsilon-equilibria

Abstract

We present efficient approximation algorithms for finding Nash equilibria in anonymous games, that is, games in which the players utilities, though different, do not differentiate between other players. Our results pertain to such games with many players but few strategies. We show that any such game has an approximate pure Nash equilibrium, computable in polynomial time, with approximation O(s^2 L), where s is the number of strategies and L is the Lipschitz constant of the utilities. Finally, we show that there is a PTAS for finding an epsilon