Efficiency and Observability with Long-run and Short-run Players

We present a general algorithm for computing the limit, as 5 -> 1, of the set of payoffs of perfect public equilibria of repeated games with long-run and shortrun players, allowing for the possibility that the players' actions are not observable by their opponents. We illustrate the algorithm with two economic examples. In a simple partnership we show how to compute the equilibrium payoffs when the folk theorem fails. In an investment game, we show that two competing capitalists subject to moral hazard may both become worse off if their firms are merged and they split the profits from the merger. Finally, we show that with short-run players each long-run player's highest equilibrium payoff is generally greater when their realized actions are observed.