Unbeatable imitation

We show that for many classes of symmetric two-player games, the simple decision rule “imitate-if-better” can hardly be beaten by any strategy. We provide necessary and sufficient conditions for imitation to be unbeatable in the sense that there is no strategy that can exploit imitation as a money pump. In particular, imitation is subject to a money pump if and only if the relative payoff function of the game is of the rock–scissors–paper variety. We also show that a sufficient condition for imitation not being subject to a money pump is that the relative payoff game is a generalized ordinal potential game or a quasiconcave game. Our results apply to many interesting examples of symmetric games including 2×2 games, Cournot duopoly, price competition, public goods games, common pool resource games, and minimum effort coordination games.