Explaining cooperative experimental evidence in the Centipede game constitutes a challenge for rational game theory. Traditional analyses of Centipede based on backward induction predict uncooperative behavior. Furthermore, analyses based on learning or adaptation under the assumption that those strategies that are more successful in a population tend to spread at a higher rate usually make the same prediction. In this paper we consider an adaptation model in which agents in a finite population do adopt those strategies that turn out to be most successful, according to their own experience. However, this behavior leads to an equilibrium with high levels of cooperation and whose qualitative features are consistent with experimental evidence.
