  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. We provide necessary and sufficient conditions for imitation to be
unbeatable and show that it can only be beaten by much in games that are of the
rock-scissors-paper variety. 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., imitation cannot be beaten by much even by a very
clever opponent.
