Knowing the Informed Player's Payoffs and Simple Play in Repeated Games

We revisit the classic model of two-player repeated games with undiscounted utility, observable actions, and one-sided incomplete information, and further assume the informed player has state-independent preferences. We show the informed player can attain a payoff in equilibrium if and only if she can attain it in the simple class of equilibria first studied by Aumann, Maschler, and Stearns (1968), in which information is only revealed in the game's initial stages. This sufficiency result does not extend to the uninformed player's equilibrium payoff set