Playing Anonymous Games using Simple Strategies
Yu Cheng, Ilias Diakonikolas, Alistair Stewart

TL;DR
This paper presents new algorithms for computing approximate Nash equilibria in anonymous games, showing polynomial-time solutions for certain approximation levels and introducing simple strategies based on probabilistic structures.
Contribution
It introduces a polynomial-time algorithm for approximate equilibria with specific bounds, and establishes a structural connection between Nash equilibria and Poisson multinomial distributions.
Findings
Polynomial-time algorithm for $O(1/n^{1- ext{delta}})$-approximate equilibria.
Faster algorithm with $ ilde O((n+k)kn^k)$ runtime for specific approximate equilibria.
Structural lemma relating Poisson multinomial distributions to approximate Nash equilibria.
Abstract
We investigate the complexity of computing approximate Nash equilibria in anonymous games. Our main algorithmic result is the following: For any -player anonymous game with a bounded number of strategies and any constant , an -approximate Nash equilibrium can be computed in polynomial time. Complementing this positive result, we show that if there exists any constant such that an -approximate equilibrium can be computed in polynomial time, then there is a fully polynomial-time approximation scheme for this problem. We also present a faster algorithm that, for any -player -strategy anonymous game, runs in time and computes an -approximate equilibrium. This algorithm follows from the existence of simple approximate equilibria of anonymous games, where each player…
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