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We present three examples of finitely repeated games with public monitoring that have sequential equilibria in private strategies, i.e., strategies that depend on own past actions as well as public signals. Such private sequential equilibria can have features quite unlike those of the more familiar perfect public equilibria: (i) making a public signal less informative can create Pareto superior equilibrium outcomes; (U) the equilibrhun finalperiod action profile need not be a stage game equilibrium; and (iii) even if the stage game has a unique correlated (and hence Nash) equilibrium, the first-period action profile need not be a stage game equilibrium. Download Paper
We describe the maximum efficient subgame perfect equilibrium payoff for a player in the repeated Prisoners' Dilemma, as a function of the discount factor. For discount factors above a critical level, every efficient, feasible, individually rational payoff profile can be sustained. For an open and dense subset of discount factors below the critical value, the maximum efficient payoff is not an equilibrium payoff. When a player cannot achieve this payoff, the unique equilibrium outcome achieving the best efficient equilibrium payoff for a player is eventually cyclic. There is an uncountable number of discount factors below the critical level such that the maximum efficient payoff is an equilibrium payoff. Download Paper
Investors making complementary investments typically do not have incentives to invest efficiently when they cannot contract with each other prior to their decisions because of the hold-up problem: when they bargain over the surplus generated by their investments, they will usually not obtain the full fruits of the investment. Intuitively, the hold-up problem should be ameliorated if, in the bargaining stage, each agent has alternatives to the partner he is bargaining with. We characterize the matching and division of surplus in finite economies for any initial investment decisions. We provide conditions on those decisions that guarantee that each agent will capture the change in the aggregate social surplus that results from any investment change he makes. We further show that for any given problem, there exists a bargaining rule by which pairs split their surplus that will support efficient investment choices in equilibrium. We also show, however, that over invest­ment or underinvestment can occur for natural bargaining rules. Download Paper
We consider a dynamic general equilibrium asset pricing model with heterogeneous agents and asymmetric information. We show how agents' different methods of gathering information affect their chances of survival in the market depending upon the nature of the information and the level of noise in the economy. Download Paper
Economists typically analyze individuals' market behavior in isolation from their nonmarket decisions. While this research strategy has generally been successful, it can lead to systematic errors when agents' nonmarket behavior affects their market choices. In this paper we analyze how individuals' investment behavior changes as a result of nonmarket behavior. Specifically, we analyze a model in which individuals must decide how to al­ locate their initial endowment between two random investments, where the returns are perfectly correlated across individuals for the first investment but independent across individuals for the second. We consider an environment in which men and women match, with wealthier individuals more successful in matching. We show how individuals' concern about relative wealth can affect their investment decisions, and we provide conditions under which individuals bias their investments either toward or away from the investment with correlated returns. A modification of the model is used to explain why agents’ investments might exhibit a home country bias. Download Paper
Do investors making complementary investments face the correct incen­tives, especially when they cannot contract with each other prior to their de­cisions? We present a two-sided matching model in which buyers and sellers make investments prior to matching. Once matched, buyer and seller bar­ gain over the price, taking into account outside options. Efficient decisions can always be sustained in equilibrium. We characterize the inefficiencies that can arise in equilibrium, and show that equilibria will be constrained efficient. We also show that the degree of diversity in a large market has implications for the extent of any inefficiency. Download Paper
In repeated games with imperfect public monitoring, players can use public signals to coordinate their behavior perfectly, and thus support cooperative outcomes with the threat of punishments. But with even a small amount of private monitoring, players’ private histories may lead them to have sufficiently different views of the world that such coordination on punishments is no longer possible (we describe a simple strategy profile that is a perfect public equilibrium of a repeated prisoner’s dilemma with imperfect public monitoring and yet is not an equilibrium for arbitrarily close games with private monitoring). If a perfect public equilibrium has players’ behavior conditioned only on finite histories, then it induces an equilibrium in all close-by games with private monitoring. This implies a folk theorem for repeated games with almost-public almost-perfect monitoring. Download Paper
This paper addresses the question of whether agents will invest efficiently in attributes that will increase their productivity in subsequent matches with other individuals. We present a two-sided matching model in which buyers and sellers make investment decisions prior to a matching stage. Once matched, the buyer and seller bargain over the transfer price. In contrast to most matching models, preferences over possible matches are affected by decisions taken before the matching process. We show that if bargaining respects the existence of outside options (in the sense that the resulting allocation is in the core of the assignment game), then efficient decisions can always be sustained in equilibrium. However, there may also be inefficient equilibria. Our analysis identifies a potential source of inefficiency not present in most matching models. Download Paper
We examine a market in which firms confront a moral hazard problem in the provision of product quality, facing a short-term incentive to produce low quality but potentially earning higher profits from “committing” to high quality. There are two types of firms in the market, “inept” firms who can produce only low quality, and “competent” firms who have a choice between high and low quality. Firms occasionally leave the market, causing competent and inept potential entrants to compete for the right to inherit the departing firm’s reputation. In a repeated interaction, with consumers receiving noisy signals of product quality, competent firms choose high quality in an attempt to distinguish themselves from inept firms. Competent firms find average reputations most valuable in the sense that a competent firm is most likely to enter the market by purchasing an average reputation, in the hopes of building it into a good reputation, than either a very low reputation or a very high reputation. Inept firms , in contrast, find it profitable to either buy high reputations and deplete them or buy low reputations. Download Paper
We construct a model in which a firm’s reputation must be built gradually, is managed, and dissipates gradually unless appropriately maintained. Consumers purchase an experience good from a firm whose unobserved effort affects the probability distribution of consumer utilities. Consumers observe private, noisy signals (consumer utilities) of the behavior of the firm, yielding a game of imperfect private monitoring. The standard approach to reputations introduces some “good” or “Stackelberg” firms into the model, with consumers ignorant of the type of the firm they face and with ordinary firms acquiring their reputations by masquerading as Stackelberg firms. In contrast, the key ingredient of our reputation model is the continual possibility that the ordinary or “competent” firm might be replaced by a “bad” or “inept” firm who never chooses the Stackelberg action. Competent firms then acquire their reputations by convincing consumers that they are not inept. Building a reputation is an exercise in separating oneself from inept firms who one is not, rather than pooling with Stackelberg firms who one would like to be. We investigate how a firm manages such a reputation, showing, among other features, that a competent firm may not always choose the most efficient effort level to distinguish itself from an inept one. Download Paper
In repeated games with imperfect public monitoring, players can use public signals to perfectly coordinate their behavior. Our study of repeated games with imperfect private monitoring focuses on the coordination problem that arises without public signals. We present three new observations. First, in a simple twice repeated game, we characterize the private signaling technologies that allow non-static Nash behavior in pure strategy equilibria. Our characterization uses the language of common p-belief due to Monderer and Samet (GDB, 1989). Second, we show that in the continuum action convention game of Shin and Williamson (GEB, 1996), for any full support private monitoring technology, equilibria of the finitely repeated convention game must involve only static Nash equilibria. By contrast, with sufficiently informative public monitoring, the multiplicity of Nash equilibria allows a finite folk theorem. Finally, for finite action games, we prove that there are full support private monitoring technologies for which a Nash reversion infinite horizon folk theorem holds. Download Paper
We consider a market in which there are two types of workers, “red” and “green,” where these labels have no direct payoff implications. Workers can choose to acquire costly skills. Skilled workers must search for firms with a job vacancy, while firms with vacancies also search for unemployed workers. A unique symmetric equilibrium exists in which firms ignore workers’ colors. There may also exist an asymmetric equilibrium in which firms only search for green worker, more green than red workers acquire skills, skilled green workers receive higher wage rates than skilled red workers, and the unemployment rate is higher among skilled red than green workers, though there are more unemployed skilled green workers than red workers. Discrimination between ex ante identical individuals thus arises as an equilibrium phenomenon. Our analysis differs from previous models of discrimination in assuming that firms have perfect information about workers with whom they are matched, and strictly prefer to hire minority workers (contingent on meeting a worker), and in generating predictions concerning unemployment as well as wage rates. Download Paper
Evolutionary game theory provides an answer to two of the central questions in economic modeling: When is it reasonable to assume that people are rational? And, when is it reasonable to assume that behavior is part of a Nash equilibrium (and if it is reasonable, which equilibrium)? The traditional answers are not compelling, and much of evolutionary modeling is motivated by the need for a better answer. Evolutionary game theory suggests that, in a range of settings, agents do (eventually) play a Nash equilibrium. Moreover, evolutionary modeling has shed light on the relative plausibility of different Nash equilibria. Download Paper
We analyze a model in which there is socially inefficient competition among people. In this model, self-enforcing social norms can potentially control the inefficient competition. However, the inefficient behavior often cannot be suppressed in equilibrium among those with the lowest income due to the ineffectiveness of sanctions against those in the society with the least to lose. We demonstrate that in such cases, it may be possible for society to be divided into distinct classes, with inefficient behavior suppressed in the upper classes but not in the lower. Download Paper
This paper shows that Nash equilibria of a local-interaction game are equivalent to correlated equilibria of the underlying game. Download Paper
We develop a simple model that captures a concern for relative standing. The concern for relative standing is instrumental in the sense that individ­ uals do not get utility directly from their relative standing, but rather, the concern is induced because relative standing affects consumption of stan­ dard commodities. We investigate the consequences of a concern for relative wealth in models in which individuals are making labor-leisure choice deci­ sions. Among the results, we show how individuals' decisions are affected by the aggregate income distribution and how the concern for relative wealth can generate behavior that can be interpreted as conspicuous consumption when wealth is not directly observable. Download Paper