  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.
