Equilibrium behaviors in repeated games

We examine a patient player's behavior when he can build reputations in front of a sequence of myopic opponents. With positive probability, the patient player is a commitment type who plays his Stackelberg action in every period. We characterize the patient player's action frequencies in equilibrium. Our results clarify the extent to which reputations can refine the patient player's behavior and provide new insights to entry deterrence, business transactions, and capital taxation. Our proof makes a methodological contribution by establishing a new concentration inequality.