"Repeated Games, Entry in The New Palgrave Dictionary of Economics, 2nd Edition"

This entry shows why self-interested agents manage to cooperate in a long-term relationship. When agents interact only once, they often have an incentive to deviate from cooperation. In a repeated interaction, however, any mutually beneficial outcome can be sustained in an equilibrium. This fact, known as the folk theorem, is explained under various information structures. This entry also compares repeated games with other means to achieve efficiency and briefly discuss the scope for potential applications.

"Weakly Belief-Free Equilibria in Repeated Games with Private Monitoring"

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), and it is shown that this class can outperform the equilibria identified by the previous work.

"The Erosion and Sustainability of Norms and Morale"

The initially high performance of a socioeconomic organization is quite often subject to gradual erosion over time. We present a simple model which captures such a phenomenon. We assume that players are partly motivated by certain psychological factors, norms and morale, and they are willing to exert extra effort if others do so. This results in a "continuum" of equilibrium effort levels, whose minimum corresponds to the Nash equilibrium with respect to the material incentives. We show that repeated random shocks induce the erosion of equilibrium e ort levels, but they do not completely decay; in the long run a certain range of efforts are sustainable. Our model shows that different organizations typically enjoy diverse norms and morale, which persist for a long time, in the vicinity of the equilibrium determined by material incentives.

"Randomization, Communication and Efficiency in Repeated Games with Imperfect Public Monitoring"

The present paper shows that the Folk Theorem under imperfect (public) information (Fudenberg, Levine and Maskin (1994)) can be obtained under much weaker set of assumptions, if we allow communication among players. Our results in particular show that for generic symmetric games with at least four players, we can drop the FLM condition on the number of actions and signals altogether and prove the folk theorem under the same condition as in the perfect monitoring case.

"Efficiency in Repeated Games Revisited: The Role of Private Strategies"

Most theoretical or applied research on repeated games with imperfect monitoring has restricted attention to public strategies; strategies that only depend on history of publicly observable signals, and perfect public equilibrium (PPE); sequential equilibrium in public strategies. The present paper sheds light on the role of private strategies; strategies that depend on players' own actions in the past as well as observed public signals. Our main finding is that players can sometimes make better use of information by using private strategies and efficiency in repeated games can often be drastically improved. We illustrate this for both games with a small signal space (Anti-folk theorem example) and games with a large signal space, for which the Folk Theorem holds. Our private strategy can be regarded as a machine which consists of two states. We provide two di erent characterizations of our two-state machine equilibrium for general two-person repeated games with imperfect public monitoring.

"Less is More: An Observability Paradox in Repeated Gamess"

We present a repeated prisoners' dilemma game with imperfect public monitoring, which exhibits the following paradoxical feature: the equilibrium payoff set expands and asymptotically achieves full efficiency as the public signal becomes less sensitive to the hiden actions of the players.

"Introduction to Repeated Games with Private Monitoring"

We present a brief overview of recent developments on discounted repeated games with (imperfect) private monitoring. The literature explores the possibility of cooperation in a long-term relationship, where each agent receives imperfect private information about the opponents' actions. Although this class of games admits a wide range of applications such as collusion under secret price-cutting, exchange of goods with uncertain quality, and observation errors, it has fairly complex mathematical structure due to the lack of common information shared by players. This is in sharp contrast to the well-explored case of repeated games under public information (with the celebrated Folk Theorems), and until recently little had been known about the private monitoring case. However, rapid developments in the past few years have revealed the possibility of cooperation under private monitoring for some class of games.

Decentralized trade, random utility and the evolution of social welfare

We study decentralized trade processes in general exchange economies and house allocation problems with and without money. The processes are subject to persistent random shocks stemming from agents' maximization of random utility. By imposing structure on the utility noise term -logit distribution-, one is able to calculate exactly the stationary distribution of the perturbed Markov process for any level of noise. We show that the stationary distribution places the largest probability on the maximizers of weighted sums of the agents' (intrinsic) utilities, and this probability tends to 1 as noise vanishe

DECENTRALIZED TRADE, RANDOM UTILITY AND THE EVOLUTION OF SOCIAL WELFARE

We study decentralized trade processes in general exchange economies and house allocation problems with and without money. The processes are subject to persistent random shocks stemming from agents’ maximization of random utility. By imposing structure on the utility noise term —logit distribution—, one is able to calculate exactly the stationary distribution of the perturbed Markov process for any level of noise. We show that the stationary distribution places the largest probability on the maximizers of weighted sums of the agents’ (intrinsic) utilities, and this probability tends to 1 as noise vanishes