Decentralized Fictitious Play Converges Near a Nash Equilibrium in Near-Potential Games

TL;DR

This paper proves that decentralized fictitious play converges near a Nash equilibrium in near-potential games, extending the convergence guarantees of standard fictitious play to a broader class of games with approximate potential functions.

Contribution

It establishes convergence of decentralized fictitious play in near-potential games, a significant generalization of existing results for potential games.

Findings

Empirical frequencies converge around a single Nash equilibrium.

Convergence holds under finite Nash equilibria and near-potential utility conditions.

Results extend fictitious play convergence to near-potential game settings.

Abstract

We investigate convergence of decentralized fictitious play (DFP) in near-potential games, wherein agents preferences can almost be captured by a potential function. In DFP agents keep local estimates of other agents' empirical frequencies, best-respond against these estimates, and receive information over a time-varying communication network. We prove that empirical frequencies of actions generated by DFP converge around a single Nash Equilibrium (NE) assuming that there are only finitely many Nash equilibria, and the difference in utility functions resulting from unilateral deviations is close enough to the difference in the potential function values. This result assures that DFP has the same convergence properties of standard Fictitious play (FP) in near-potential games.