Why Imitate, and if so, How? A Bounded Rational Approach to Multi-Armed Bandits

We consider the situation in which individuals in a finite population must repeatedly choose an action yielding an uncertain payoff. Between choices, each individual may observe the performance of one other individual. We search for rules of behavior with limited memory that increase expected payoffs for any underlying payoff distribution. It is shown that the rule that outperforms all other rules with this property is the one that specifies imitation of the action of an individual that performed better with a probability proportional to how much better she performed. When each individual uses this best rule, the aggregate population behavior can be approximated by the replicator dynamic.