Learning from average experience

We study repeated interaction over time and explore long-run behavior when individuals imitate successful past performers, selecting actions that yielded better average historical performance. For a class of environments (such as the oligopoly environment) it is known that such behavior results in very inefficient outcomes. Increasing ones own payoff comes partly at the expense of others and the dynamics generated by imitative behavior lead to low welfare in the long run. We show that this conclusion rests on the assumption that individuals have short memories. The situation differs sharply if agents have longer memories and evaluate actions according to average performance. In that case, it turns out that highly cooperative or collusive arise. In particular, with sufficiently long memory the unique stochastically stable outcome is the maximally collusive outcome.