Convergence of best-response dynamics in extensive-form games

Abstract

This paper presents a collection of convergence results on best-response dynamics in extensive-form games. We prove that in all finite generic extensive-form games of perfect information, every solution trajectory to the continuous-time best-response dynamic converges to a Nash equilibrium component. We show the robustness of this convergence in the sense that along any interior approximate best-response trajectory, the evolving state is close to the set of Nash equilibria most of the time. We also prove that in any perfect-information game in which every play contains at most one decision node of each player, any interior approximate best-response trajectory converges to the backward-induction strategy profile. Our final result concerns self-confirming equilibria in perfect-information games. If each player always best responds to her conjecture of the current strategy profile, and she updates her conjecture based only on observed moves, then the dynamic will converge to the set of self-confirming equilibria.