  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.
