Why Imitate, and If So, How? A Boundedly Rational Approach to Multi-armed Bandits

Individuals in a finite population repeatedly choose among actions yielding uncertain payoffs. Between choices, each individual observes the action and realized outcome of one other individual.We restrict our search to learning rules with limited memorythat increase expected payoffs regardless of the distributionunderlying their realizations. It is shown that the rule thatoutperforms all others is that which imitates the action ofan observed individual (whose realized outcome is better thanself) with a probability proportional to the difference in theserealizations. When each individual uses this best rule,the aggregate population behavior is approximated by thereplicator dynamic. Journal of Economic Literature ClassificationNumbers: C72, C79, D83.Copyright 1998 Academic Press.