Fictitious Play in Potential Games

07/19/2017

∙

by   Brian Swenson, et al.

∙

0

∙

share

This work studies the convergence properties of continuous-time fictitious play in potential games. It is shown that in almost every potential game and for almost every initial condition, fictitious play converges to a pure-strategy Nash equilibrium. We focus our study on the class of regular potential games; i.e., the set of potential games in which all Nash equilibria are regular. As byproducts of the proof of our main result we show that (i) a regular mixed-strategy equilibrium of a potential game can only be reached by a fictitious play process from a set of initial conditions with Lebesgue measure zero, and (ii) in regular potential games, solutions of fictitious play are unique for almost all initial conditions.