Fictitious Play in Potential Games

07/19/2017
by   Brian Swenson, et al.
0

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.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset