A patient player privately observes a persistent state and interacts with an infinite sequence of myopic uninformed players. The patient player is either a strategic type who maximizes his payoff or one of several commitment types who mechanically play the same action in every period. I focus on situations in which the uninformed player's best reply to a commitment action depends on the state and where the total probability of commitment types is sufficiently small. I show that the patient player's equilibrium payoff is bounded below his commitment payoff in some equilibria under some of his payoff functions. This is because he faces a trade‐off between building his reputation for commitment and signaling favorable information about the state. When players' stage‐game payoff functions are monotone‐supermodular, the patient player receives high payoffs in all states and in all equilibria. Under an additional condition on the state distribution, my reputation model yields a unique prediction on the patient player's equilibrium payoff and on‐path behavior.