I study a reputation model in which a patient player privately observes a persistent state that  affects his myopic opponents' payoffs, and can be one of the several commitment types that plays the same (possibly mixed ) action over time. The main result is a characterization of the set of environments under which the patient player obtains at least his commitment payoff in all equilibria regardless of his stage-game payoff function. My result implies that small perturbations to a pure commitment action can lead to a discontinuous change in the patient player's equilibrium payoff. The main technical contribution is to use martingale techniques to construct a non-stationary strategy under which the patient player can avoid signaling negative information about the state while at the same time, matching the long-run frequency of his actions to the mixed commitment action and convincing his opponents that his action is close to the commitment action in almost all periods .
A patient player privately observes a persistent state that directly affects his myopic opponents' payoffs, and can be one of the several commitment types that plays the same mixed action in every period. I characterize the set of environments under which the patient player obtains at least his commitment payoff in all equilibria regardless of his stage-game payoff function. Due to interdependent values, the patient player cannot guarantee his mixed commitment payoff by imitating the mixed-strategy commitment type, and small perturbations to a pure commitment action can significantly reduce the patient player's guaranteed equilibrium payoff .
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I study a reputation model in which a
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directly
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(possibly mixed ) action over time. The main result is a characterization of
mixed action in every period. I characterize
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My result implies that
Due to interdependent values, the patient player cannot guarantee his mixed commitment payoff by imitating the mixed-strategy commitment type, and
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lead to a discontinuous change in
significantly reduce
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equilibrium payoff. The main technical contribution is to use martingale techniques to construct a non-stationary strategy under which the patient player can avoid signaling negative information about the state while at the same time, matching the long-run frequency of his actions to the mixed commitment action and convincing his opponents that his action is close to the commitment action in almost all periods
guaranteed equilibrium payoff