On the Evolution of Imitative Behavior

We analyze the evolution of behavioral rules for learning how to play a two-armed bandit. Individuals have no information about the underlying pay-off distributions and have limited memory about their own past experience. Instead they must rely on information obtained trough observing the performance of other individuals. Evolution is modelled using the replicator dynamic with the revision behaviors as replicators. We find that evolution favors a special class of imitative rules. These so-called strictly improving rules, that also play an important role in a bounded rational selection approach (Schlag [16]), are found to be neutrally stable when facing any two-armed bandit.