This paper characterizes long-run outcomes for broad classes of symmetric games, when players select actions on the basis of average historical performance. Received wisdom suggests that when agent's interests are partially opposed, behavior is excessively competitive: "keeping up with the Jones'[thin space]" lowers everyones' welfare. Here, we study the long-run consequences of imitative behavior when agents have sufficiently long memories and evaluate past actions in terms of (weighted) average payoff. Imitation robustly leads to cooperative outcomes (with highest symmetric payoffs) in the long run. Furthermore, lengthening memory reinforces this effect. This provides a rationale, for example, for collusive cartel-like behavior without collusive intent.
