Attainable payoffs in repeated games with interdependent private information. Working paper

In this paper I prove two folk theorems for repeated games with private information and communication, in which signal spaces may be arbitrary, signals may be statisti-cally interdependent, and payoffs for each player may depend on the signals of other players. (1) In games with transferable utility, if an outcome rule (i) is potentially in-dividually rational and can be implemented by an (ii) interim incentive compatible and (iii) ex post budget balanced mechanism in the stage game, then the level of aggregate utility it provides can also be implemented as the average aggregate utility of a sta-tionary perfect public equilibrium in the infinitely repeated game, given a sufficiently high discount factor. (2) In games without transferable utility, if an expected payoff profile (i) is individually rational and (ii) can be implemented by an interim incentive compatible mechanism in the stage game, if (iii) the convex hull of such payoff pro-files has non-empty interior, and (iv) if the probability measure over signals satisfies a condition guaranteeing ex post weighted budget balance, then the payoff profile can be approximated as the average utility profile of a PPE in the infinitely repeated game, as the discount factor approaches unity. Finally, I show that the condition guaranteeing ex post weighted budget balance, (iv), is satisfied by both independent and globally interdependent probability measures