The present paper tries to explain cooperative behavior in an organization run by a sequence of long- but finitely-lived agents. The author shows that the Folk theorem holds for infinitely repeated games with overlapping generations of finitely-lived players; any mutually beneficial outcome can approximately be sustained if the player's life span and the overlapping periods are long enough. The result is stronger than the usual Folk theorems in that it employs no assumption on the stage game, such as the full dimensionality of payoff set or multiplicity of equilibria.

The present paper extends the theory of self-enforcing agreements in a long-term relationship (the Folk Theorem in repeated games) to the situation where agents change their partners over time. Cooperation is sustained because defection against one agent causes sanction by others, and the paper shows how such a “social norm” is sustained by self-interested agents under various degrees of observability. Two main results are presented. The first one is an example where a community can sustain cooperation even when each agent knows nothing more than his personal experience. The second shows a Folk Theorem that the community can realize any mutually beneficial outcomes when each agent carries a label such as reputation, membership, or licence, which are revised in a systematic way.

The present paper formalizes the idea that improved monitoring helps coordination in long term relationships. Specifically, the pure-strategy sequential equilibrium payoff set is shown to expand (in the sense of set inclusion) in repeated games with inperfect monitoring, when the quality of the signal improves in Blackwell's sense. Furthermore, the directions of the expansion are identified.

The supergame-theoretic model of price competition (Rotemberg and Saloner, 1986) is reexamined in the case of serially correlate demand shocks. The equilibrium price is shown to exhibit the same counter-cyclical movement as the i.i.d. case if the discount factor and the number of firms satisfy a certain relationship.

Repeated games with imperfect private monitoring have a wide range of applications, but a complete characterization of all equilibria in this class of games has yet to be obtained. The existing literature has identified a relatively tractable subset of equilibria. The present paper introduces the notion of weakly belief-free equilibria for repeated games with imperfect private monitoring. This is a tractable class which subsumes, as a special case, a major part of the existing literature (the belief-free equilibria). It is shown that this class can outperform the equilibria identified by the previous work.

We analyze an evolutionary model with a finite number of players and with noise or mutations.The expansion and contraction of strategies is linked-as usual-to their current relative success, but mutations-which perturb the system away from its deterministic evolution-are present as well.Mutations can occur in every period, so the focus is on the implications of ongoing mutations, not a one-shot mutation.The effect of these mutations is to drastically reduce the set of equilibria to what we term "long-run equilibria."For 2 x 2 symmetric games with two symmetric strict Nash equilibria the equilibrium selected satisfies (for large populations) Harsanyi and Selten's (1988) criterion of risk-dominance.In particular, if both strategies have equal security levels, the Pareto dominant Nash equilibrium is selected, even though there is another strict Nash equilibrium.

This paper proposes a class of games called revision games . In a revision game, players start with initially prepared actions, followed by a sequence of random revision opportunities until a predetermined deadline. In the course of revisions, players monitor each other's behavior. It is shown that players can cooperate and that their behavior under the optimal equilibrium is described by a simple differential equation. We present the necessary and sufficient conditions for cooperation to be sustained in revision games. We also present applications to the preopening activities in the stock exchange and to an electoral campaign.

Most theoretical or applied research on repeated games with imperfect monitoring has focused on public strategies: strategies that depend solely on the history of publicly observable signals. This paper sheds light on the role of private strategies: strategies that depend not only on public signals, but also on players' own actions in the past. Our main finding is that players can sometimes make better use of information by using private strategies and that efficiency in repeated games can be improved. Our equilibrium private strategy for repeated prisoners' dilemma games consists of two states and has the property that each player's optimal strategy is independent of the other player's state.

The authors examine discounted repeated games where players privately observe different signals. A leading example is secret price cutting; a firm cannot directly observe rival firms' price cutting but its own sales can imperfectly indicate what is going on. The characterization of equilibria in this class of games has been an open question. The authors construct equilibria where players voluntarily communicate what they have observed and prove folk theorems. Their results thus provide a theoretical support for the conventional wisdom that communication facilitates collusion.