Unbeatable Imitation

We show that for many classes of symmetric two-player games, the simple decision rule \imitate-the-best" can hardly be beaten by any other decision rule. Weprovide necessary and sufficient conditions for imitation to be unbeatable and showthat it can only be beaten by much in games that are of the rock-scissors-papervariety. Thus, in many interesting examples, like 2x2 games, Cournot duopoly,price competition, rent seeking, public goods games, common pool resource games,minimum effort coordination games, arms race, search, bargaining, etc., imitationcannot be beaten by much even by a very clever opponent.[...]