Beatable imitation in symmetric games with perturbed payoffs

•“Imitate-if-better” has been shown to be unbeatable in a large class of games.•Introduce random perturbations in the payoffs.•Characterize the class of perturbed games for which imitation can be exploited.•Result may hold even for arbitrarily small perturbations.•Reason why imitation might not be reasonable heuristic in changing environments.

In a recent paper, Duersch et al. (2012) showed that in a rather broad class of repeated symmetric two-player games, a player who uses the simple “imitate-if-better” heuristic cannot be subject to a money pump. In this paper, we extend the analysis to games with randomly perturbed payoffs and we show that this result is not robust to, even arbitrarily small, payoff perturbations. In particular, we provide a necessary and sufficient condition that characterizes the class of perturbed games in which the imitator can be subject to a money pump.