Once Beaten, Never Again: Imitation in Two-Player Potential Games

Abstract

We show that in symmetric two-player exact potential games, the simple decision rule "imitate-if-better" cannot be beaten by any strategy in a repeated game by more than the maximal payoff difference of the one-period game. Our results apply to many interesting games including examples like 2x2 games, Cournot duopoly, price competition, public goods games, common pool resource games, and minimum effort coordination games.Imitate-the-best, learning, exact potential games, symmetric games, relative payoffs, zero-sum games