Decentralized Fictitious Play in Near-Potential Games with Time-Varying Communication Networks

TL;DR

This paper analyzes the convergence of decentralized fictitious play in near-potential games with dynamic communication networks, showing it converges similarly to standard fictitious play in ideal conditions.

Contribution

It extends fictitious play analysis to near-potential games with time-varying networks, demonstrating convergence guarantees under decentralized information sharing.

Findings

Empirical frequencies converge to strategies with high potential function values.

Convergence guarantees are similar to those in standard fictitious play.

Results hold even with dynamic, local communication networks.

Abstract

We study the convergence properties of decentralized fictitious play (DFP) for the class of near-potential games where the incentives of agents are nearly aligned with a potential function. In DFP, agents share information only with their current neighbors in a sequence of time-varying networks, keep estimates of other agents' empirical frequencies, and take actions to maximize their expected utility functions computed with respect to the estimated empirical frequencies. We show that empirical frequencies of actions converge to a set of strategies with potential function values that are larger than the potential function values obtained by approximate Nash equilibria of the closest potential game. This result establishes that DFP has identical convergence guarantees in near-potential games as the standard fictitious play in which agents observe the past actions of all the other agents.