Dilip Abreu

On the Theory of Infinitely Repeated Games with Discounting

This paper presents a systematic framework for studying infinitely-repeated games with discounting, focusing on pure strategy (subgame) perfect equilibria. It introduces a number of concepts whi ch organize the theory in a natural way. These include the idea of an optimal penal code, and the related notions of simple penal codes an d simple strategy profiles. Copyright 1988 by The Econometric Society.

Bubbles and Crashes

We present a model in which an asset bubble can persist despite the presence of rational arbitrageurs. The resilience of the bubble stems from the inability of arbitrageurs to temporarily coordinate their selling strategies. This synchronization problem together with the individual incentive to time the market results in the persistence of bubbles over a substantial period of time. Since the derived trading equilibrium is unique, our model rationalizes the existence of bubbles in a strong sense. The model also provides a natural setting in which public events, by enabling synchronization, can have a disproportionate impact relative to their intrinsic informational content.

Optimal Cartel Equilibria with Imperfect monitoring

There exist optimal symmetric equilibria in the Green-Porter model [5, 8] having an elementary intertemporal structure. Such an equilibrium is described entirely by two subsets of price space and two quantities, the only production levels used by firms in any contingency. The central technique employed in the analysis is the reduction of the repeated game to a family of static games.

Extremal equilibria of oligopolistic supergames

General propositions established in Abreu (Ph.D. thesis, Princeton University, October 1983) are applied to the analysis of optimal punishments and constrained Pareto optimal paths of symmetric oligopolistic supergames. A remarkably simple 2-dimensional stick-and-carrot characterization of optimal symmetric punishments is obtained. An analogous result holds for the general case of asymmetric punishments, motivating the study of asymmetric Pareto optimal paths. The latter turn out to have a highly non-stationary dynamic structure which sometimes entails intertemporal reversals of relative payoffs between firms.

Synchronization risk and delayed arbitrage

We argue that arbitrage is limited if rational traders face uncertainty about when their peers will exploit a common arbitrage opportunity. This synchronization risk—which is distinct from noise trader risk and fundamental risk—arises in our model because arbitrageurs become sequentially aware of mispricing and they incur holding costs. We show that rational arbitrageurs ‘‘time the market’’ rather than correct mispricing right away. This leads to delayed arbitrage. The analysis suggests that behavioral influences on prices are resistant to arbitrage in the short and intermediate run. r 2002 Elsevier Science B.V. All rights reserved.

Information and Timing in Repeated Partnerships

In a repeated partnership game with imperfect monitoring, the authors distinguish among the effects of (1) reducing the interest rate, (2) shortening the period over which actions are held fixed, and (3) shortening the lag with which accumulated information is reported. All three changes are equivalent in games with perfect monitoring. With imperfect monitoring, reducing the interest rate always increases the possibilities for cooperation, but the other two changes always have the reverse effect when the interest rate is small. Copyright 1991 by The Econometric Society.

VIRTUAL IMPLEMENTATION IN NASH EQUILIBRIUM

Consider a social choice correspondence as a mapping from preference profiles to lotteries over some finite set of alternatives. A virtually implementable social choice function in Nash equilibrium is defined, under mild domain restrictions it is shown that in societies with at least three individuals all social choice correspondences are virtually implementable in Nash equilibrium. This contrasts with Maskins classic characterization, which requires monotonicity as a necessary condition for exact implementation in Nash equilibrium. The two person case is considered seperately. While not all two-person social choice functions are virtually implementable, our necessary and sufficient condition is simple, which contrasts with the complex necessary and sufficient conditions for exact implementation. Copyright 1991 by The Econometric Society.

Subgame perfect implementation: A necessary and almost sufficient condition

We present a necessary and almost sufficient condition for subgame perfect implementation of social choice correspondences. In societies with at least three individuals, any social choice correspondence which satisfies no veto power and our necessary Condition α is subgame perfect implementable. Thus Condition α is analogous to monotonicity which, by Maskins celebrated characterization, is necessary and, in a similar way, almost sufficient for Nash implementation.

Bargaining and Efficiency in Networks

We study an infinite horizon game in which pairs of players connected in a network are randomly matched to bargain over a unit surplus. Players who reach agreement are removed from the network without replacement. The global logic of efficient matchings and the local nature of bargaining, in combination with the irreversible exit of player pairs following agreements, create severe hurdles to the attainment of efficiency in equilibrium. For many networks all Markov perfect equilibria of the bargaining game are inefficient, even as players become patient. We investigate how incentives need to be structured in order to achieve efficiency via subgame perfect, but non-Markovian, equilibria. The analysis extends to an alternative model in which individual players are selected according to some probability distribution, and a chosen player can select a neighbor with whom to bargain.

Markov equilibria in a model of bargaining in networks

We study the Markov perfect equilibria (MPEs) of an infinite horizon game in which pairs of players connected in a network are randomly matched to bargain. Players who reach agreement are removed from the network without replacement. We establish the existence of MPEs and show that MPE payoffs are not necessarily unique. A method for constructing pure strategy MPEs for high discount factors is developed. For some networks, we find that all MPEs are asymptotically inefficient as players become patient.