Empirical Analysis of Fictitious Play for Nash Equilibrium Computation in Multiplayer Games

TL;DR

This paper empirically demonstrates that fictitious play can effectively approximate Nash equilibria in multiplayer games, outperforming regret minimization in certain scenarios and solving challenging problems where standard methods fail.

Contribution

It provides the first positive empirical evidence of fictitious play's effectiveness in multiplayer and non-zero-sum games, including challenging cases.

Findings

Fictitious play improves Nash approximation over regret minimization.

Multiple random initializations enable solving challenging convergence problems.

Fictitious play successfully addresses classical counterexamples like Shapley's.

Abstract

While fictitious play is guaranteed to converge to Nash equilibrium in certain game classes, such as two-player zero-sum games, it is not guaranteed to converge in non-zero-sum and multiplayer games. We show that fictitious play in fact leads to improved Nash equilibrium approximation over a variety of game classes and sizes than (counterfactual) regret minimization, which has recently produced superhuman play for multiplayer poker. We also show that when fictitious play is run several times using random initializations it is able to solve several known challenge problems in which the standard version is known to not converge, including Shapley's classic counterexample. These provide some of the first positive results for fictitious play in these settings, despite the fact that worst-case theoretical results are negative.