Imitation and Minimax Regret

Myopic individuals belonging to an infinite population repeatedly and independently have to choose one of two actions. Between choices each individual is informed about the success of one random other individual. We search among rules with a single round of memory for a rule that attains minimax regret in each round when all others use this rule. Behavior will not be imitative in round two but can be imitative starting round three. A simple linear imitation rule even causes all to learn the best action in the long run. The informational setting is varied to further investigate the role of imitation