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A patient player privately observes a persistent state that directly affectshis myopic opponents' payoffs, and can be one of the several commitment typesthat plays the same mixed action in every period. I characterize the set ofenvironments under which the patient player obtains at least his commitmentpayoff in all equilibria regardless of his stage-game payoff function. Due tointerdependent values, the patient player cannot guarantee his mixed commitmentpayoff by imitating the mixed-strategy commitment type, and small perturbationsto a pure commitment action can significantly reduce the patient player'sguaranteed equilibrium payoff.

Reputation for Playing Mixed Actions: A Characterization Theorem