We characterize the class of symmetric two-player games in which tit-for-tat cannot be beaten even by very sophisticated opponents in a repeated game. It turns out to be the class of exact potential games. More generally, there is a class of simple imitation rules that includes tit-for-tat but...

We report results of experiments designed to test the predictions of the best-reply process. In a Cournot oligopoly with four firms, the best-reply process should theoretically explode if demand and cost functions are linear. We find, however, no experimental evidence of such instability....