Beatable Imitation in Symmetric Games with Perturbed Payoffs

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