The rate of convergence of continuous fictitious play★

Summary The rate of convergence to Nash equilibrium of continuous fictitious play is determined for a generic set of utilities and initial beliefs in 2 x 2 games. In addition, an example is provided comparing the rate of convergence of discrete fictitious play to the rate for continuous fictitious play. Finally, the convergent dynamic of fictitious play is related to the nonconvergent gradient process dynamic in 2 x 2 games.I would like to thank Jim Jordan for many helpful discussions and for detailed comments on this paper. I also thank an anonymous referee for several helpful suggestions.