Payoff Performance of Fictitious Play

TL;DR

This paper analyzes the payoff performance of continuous-time fictitious play in two-player games, showing it often surpasses Nash equilibrium payoffs and converges to coarse correlated equilibria, with conditions where Nash dominates.

Contribution

It demonstrates that fictitious play can outperform Nash equilibrium in terms of average payoff and establishes linear equivalence to such games, extending understanding of equilibrium dynamics.

Findings

Fictitious play often outperforms Nash equilibrium in payoff.

Fictitious play converges to coarse correlated equilibria.

Conditions identified where Nash equilibrium payoff dominates.

Abstract

We investigate how well continuous-time fictitious play in two-player games performs in terms of average payoff, particularly compared to Nash equilibrium payoff. We show that in many games, fictitious play outperforms Nash equilibrium on average or even at all times, and moreover that any game is linearly equivalent to one in which this is the case. Conversely, we provide conditions under which Nash equilibrium payoff dominates fictitious play payoff. A key step in our analysis is to show that fictitious play dynamics asymptotically converges the set of coarse correlated equilibria (a fact which is implicit in the literature).