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We examine a general equilibrium model with asymetrically informed agents. The presence of asymmetric information generally presents a conflict between incentive compatibility and Pareto efficiency. We present a notion of informational size and show that the conflict between incentive compatibility and efficiency can be made arbitrarily small if agents are succinctly small informational. Download Paper
This paper studies the repeated prisoner’s dilemma with private monitoring for arbitrary number of players. It is shown that a mixture of a grim trigger strategy and permanent defection can achieve an almost efficient outcome for some range of discount factors if private monitoring is almost perfect and the number of players is large. This result also holds when the number of players is two for any prisoner’s dilemma as long as monitoring is almost perfect and symmetric. A detailed characterization of this sequential equilibrium is provided. Download Paper
This paper proposes a new solution concept to three-player coalitional bargaining problems where the underlying economic opportunities are described by a partition function. This classic bargaining problem is modeled as a dynamic non-cooperative game in which players make conditional or unconditional offers, and coalitions continue to negotiate as long as there are gains from trade. The theory yields a unique stationary perfect equilibrium outcome—the negotiation value—and provides a unified framework that selects an economically intuitive solution and endogenous coalition structure. For such games as pure bargaining games the negotiation value coincides with the Nash bargain- ing solution, and for such games as zero-sum and majority voting games the negotiation value coincides with the Shapley value. However, a novel situation arises where the out- come is determined by pairwise sequential bargaining sessions in which a pair of players forms a natural match. In addition, another novel situation exists where the outcome is determined by one pivotal player bargaining unconditionally with the other players, and only the pairwise coalitions between the pivotal player and the other players can form. Download Paper
When a monopolist asks consumers to choose a particular nonlinear tariff option, consumers do not completely know their type. Their valuations of the good and/or optimal quantity purchases are only fully realized after the optional tariff has been subscribed. In order to characterize the menu of optimal nonlinear tariffs when consumers demands are stochastic, I assume that the distributions of the different components of consumers’ types are log–concave to prove that the convolution distribution of these components is increasing hazard rate. This result, together with very weak assumptions on demand (common to standard nonlinear pricing), ensures that the continuum of optional nonlinear tariffs is characterized by quantity discounts. I test nonparametrically the model using data directly linked to consumer types from the 1986 Kentucky telephone tariff experiment. I show that the distri- bution of actual calls second order stochastically dominates the distribution of expected calls, which fully supports the suggested type–varying theoretical model. Finally, I analyze possible welfare effects of the introduction of optional tariffs and their relative expected profitability using the empirical distribution of consumer types in two local exchanges with differentiated calling patterns. The evidence suggests that a menu of optional two–part tariffs dominate any other pricing strategy. 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
We consider a variety of vintage-capital models of a firm's choice of technology under uncertainty in the presence of adjustment costs and technology-specific learning. Similar models have been studied in a deterministic setting. Part of our objective is to examine the robustness of the implications of the certainty models to uncertainty. Our analysis highlights the role of the specification of costs of adjustment: if an adjustment cost comes only in terms of accumulated technology-specific expertise (cf. Parente (1994)), we prove that the implications are robust for a variety of specifications of the firm's production function, however, once a cost paid in units of the produced good is introduced, predictions of an uncertainty model become increasingly different as uncertainty increases. Tractability of our models allows us to disentangle the effects of the models' assumptions, provide characterization of optimal policies, demonstrate the impact of uncertainty on the frequency of technology adoptions and growth in the economy, and present comparative statics. Download Paper
African American motorists in the United States are more likely than white motorists to have their cars searched by police checking for illegal drugs and other contraband. The courts are faced with the task of deciding on the basis of traffic-stop data whether police are basing their decisions to stop cars on the race of the driver. We develop a model of law enforcement for a popula- tion with two racial types who also differ along other dimensions relevant to criminal behavior. We discuss why a simple test commonly applied by the courts is inadequate when the econometrician observes only a subset of the characteristics observed by the policemen. Next, we show how to construct a test for whether differential treatment is motivated purely out of efficiency grounds, i.e. to maximize the number of arrests, or rejects racial prejudice. The test is valid even when the set of characteristics observed by the police- men are only partially observable by the econometrician. We apply the tests for discrimination to traffic stop data from Maryland. Finally, we present a simple analysis of the tradeoff between efficiency and fairness. Download Paper
According to Pareto, the distribution of income depends on “the nature of the people comprising a society, on the organization of the latter, and, also, in part, on chance.” An overlapping generations model of marriage, fertility and income distribution is developed here. The “nature of the people” is captured by attitudes toward marriage, divorce, fertility, and children. Singles search for mates in a marriage market. They are free to accept or reject marriage proposals. Married agents make their decisions through bargaining about work, and the quantity and quality of children. They can divorce. Social policies, such as child tax credits or child support requirements, reject the “organization of the (society).” Finally, “chance” is modelled by randomness in income, opportunities for marriage, and marital bliss. Download Paper
A moral hazard model with renegotiation is studied in which contracts must satisfy two natural restrictions, limited liability and monotonicity of payments. After he has chosen his effort, and before its consequence is realized, a risk averse entrepreneur (agent) may renegotiate his contract with a risk neutral investor (principal). Assuming the agent has the renegotiation bargaining power, a debt contract is the optimal initial contract. Download Paper
The Ellsberg paradox demonstrates that people’s belief over uncertain events might not be representable by subjective probability. We relate this paradox to other commonly observed anomalies, such as a rejection of the backward induction prediction in the one-shot Ultimatum Game. We argue that the pattern common to these observations is that the behavior is governed by “rational rules”. These rules have evolved and are optimal within the repeated and concurrent environments that people usually encounter. When an individual relies on these rules to analyze one-shot or single circumstances, paradoxes emerge. We show that when a risk averse individual has a Bayesian prior and uses a rule which is optimal for simultaneous and positively corre- lated ambiguous risks to evaluate a single vague circumstance, his behavior will exhibit uncertainty aversion. Thus, the behavior predicted by Ellsberg may be explained within the Bayesian expected utility paradigm. Download Paper
I consider repeated games with both moral hazard and adverse selection where a continuum of agents compete. It is shown that equilibria with reputation -where high effort is always exerted- may be sustained under imperfect information; the existence of such equilibria contradicts the standard results without competition. An explicit characterization of these equilibria is provided, as a discussion of the role of the environment. Download Paper
We consider the dynamic private provision of funds to projects that generate flows of public benefits. Participants have complete information about the environment, but imperfect information about individual actions: each period they observe only the aggregate contribution. Each player may contribute any amount in any period before the contributing horizon is reached. All Nash equilibrium outcomes are characterized. In many cases they are all also perfect Bayesian equilibrium outcomes. If the horizon is long, if the players’ preferences are similar, and if they are patient or the period length is short, perfect Bayesian equilibria exist that essentially complete the project. In some of them the completion time shrinks to zero with the period length – efficiency is achieved in the limit. Download Paper
In this paper we develop a quantitative theory of earnings and wealth inequality that accounts for the U.S. earnings and wealth distributions almost exactly, and we use this theory to measure the steady-state trade-offs that arise when switching from the current progressive income tax system, to a tax system in which income is proportionally taxed. Our theory is based on households that face an uninsurable idiosyncratic process on wages, that go through the life cycle stages of retirement and death, and that have altruistic feelings towards their progenie. Moreover, unlike some of the recent research on wealth inequality, the households in our model economies are equally patient. The main steady-state trade-offs implied by our policy experiment are the following: on the one hand we find that output, wealth and, to a very small extent, the labor input are higher in the model economy with proportional income taxes (4.4, 11.4 and 0.9% higher, respectively). On the other hand we find that in this model economy the distributions of wealth and consumption are significantly more unequal (their Gini indices increase by 10.4 and 13.0%, respectively). Finally, we find that the inequality of earnings and the earnings and wealth mobility of households remain almost unchanged. 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
We study a simple model of pre-electoral opinion formation that posits that interaction between neighbouring voters leads to bandwagons in the dynamics of the individual process, as well as in that of the aggregate process. We show that in different specifications of the model, there is a tendency for the process to show consensus, i.e. to approach a configuration of homogeneous support for one candidate, out of the two who run the electoral campaign. We point out that the process displays the feature that, after long time spans, a sequence of states occur which, when viewed locally, remain almost stationary and are characterized by large clusters of individuals of the same opinion. Download Paper
This paper studies a simple dynamic model of pre-electoral opinion formation, where individuals repeatedly form their opinions as to which (out of two) candidate to support. The behavioral rules we analyze allow for various forms of discontinuities, that we characterize in terms of threshold, and are defined in a locally interactive setting. We focus on both the long-run and short-run behavior of the process. It is shown that the asymptotics of the process depend crucially on the particular form of discontinuity that we postulate. In particular the process may show a tendency towards consensus, in the sense that all individuals conform in their opinion, or the system may be absorbed in configurations in which different opinions co-exist. We finally analyze various forms of asymmetries in the threshold. Download Paper
We discuss a fundamental trade-off in the political process that can lead to inefficient provision of public goods: politicians may not offer to provide socially desirable public goods because the benefits of the public good cannot be targeted to voters as easily as pork barrel spending. We study how this inefficiency is affected by alternative ways of conducting elections. We first compare a winner-take-all system with a proportional system. We then contrast two different ways of electing politicians to nationwide offices: one is majority rule, the other is the system used in U.S. presidential elections: the electoral college. 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
The paper develops a framework for the analysis of finite n-player games, recurrently played by randomly drawn n-tuples of players, from a finite population. We first relate the set of equilibria of this game to the set of correlated equilibria of the underlying game, and then focus on learning processes modelled as Markovian adaptive dynamics. For the class of potential games, we show that any myopic-best reply dynamics converges (in probability) to a correlated equilibrium. We also analyze noisy best reply dynamics, where players’ behaviour is perturbed by payoff dependent mistakes, and explicitly characterize the limit distribution of the perturbed game in terms of the correlated equilibrium payoff of the underlying game. Download Paper
While most studies on immigration focus on its impact on the labor market, in this study we address its effect on socioeconomic gaps. By studying Israeli immigration,m we examine the effects of mass immigration on socioeconomic gaps among generations using the Israeli Censuses for 1961 and 1983. We look at the socioeconomic gaps within two difference economic systems within the same economy. One system is perfect competition oriented while the second, the kibbutz, is organized as a labor-managed firm. Both generations distinguished between the different ethnic groups and the parents' country of origin. In particular, three groups are examined, in the first generation using the 1961 census, those who were born in Asian and African countries, in European and American countries, and in Israel. In the second generation, using the 1983 census, we look at those whose fathers were born in the respective areas. The analysis decomposes the Occupation Socioeconomic Score (OSS) differentials into human capital and market evaluation differences for each generation separately. The model develops a gap function that quanti ̄es the socioeconomic gaps and uses iso-gap curves to compare pre-immigration and post-immigration gaps.The study finds that the score differentials among the examined groups in the kibbutz are lower than in the city, prior to the second wave of immigration. Even after the second wave of immigration the score differentials in the kibbutz, among the examined groups, are lower than in the city. We attempt to explain this occurrence by looking at how society in the kibbutz differs in the treatment of immigrants. In particular, we focus on how the kibbutz, because of its size and reward structure, is able to internalize certain externalities and aim at a relatively higher level of education for all. Download Paper
"No Trade" Theorems claim that the mere arrival of new information can not induce trade between rational agents, even in the presence of asymmetric information. We analyze an economy in which the information agents receive is without noise. As long as preferences abide by the Sure Thing Principle, the no-trade result holds. However, under more general preferences, which do not satisfy the Sure Thing Principle, we find that dynamic consistency is a necessary but might not be a sufficient condition for information not to induce trade, even with noiseless information. We provide sufficient conditions for a No-Trade. Theorem and investigate the pattern of trade with and without dynamic consistency of preferences. Download Paper
This paper shows that the economic policies of the US and Japan have led to disequilibrium in the pattern of trade. Both economies have built-in mechanisms tending towards equilibrium. However, with restrictive policies imposed by these countries, disequilibrium is perpetuated. The US "suffers" a trade deficit, while Japan enjoys" a trade surplus. Although a trade surplus has a positive connotation, the prevailing strong yen hurts the Japanese economy. With a more integrated world, countries can no longer be concerned solely about their own economies. The recession in Japan is partially caused by this large imbalance in trade since the strong yen is driving out many Japanese businesses that can no longer compete. The large government deficit in the United States will also affect the exchange rate and the rest of the world, since the possibility of a default may raise the interest rates as well as the level of uncertainty. Countries must cooperate with each other in order to allow the world economy to reach its equilibrium. Intervention polices require that the citizens in each country actually trust that governments are committed to resolve the enigma of the strong Yen (endaka). Without strong conviction by the public that the policy would be seriously implemented, the exchange rates will not change in the desired direction. 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
This paper documents the delayed adoption of a major technological innovation: the adoption of the diesel locomotive in the US rail­ way industry. Contrary to other instances of major technological innovations, the delay in the adoption of the diesel locomotive was not associated with an initial slump in output. We provide a theoretical model which is consistent with both an increase and a decrease in output following the invention of a new technology. Within this model we identify the key factors that make a slump in output unlikely. Download Paper
In this paper, we model the dynamic portfolio choice problem facing banks, calibrate the model using empirical data from the banking industry for 1984-1993, and assess quantitatively the impact of recent regulatory. developments related to bank capital. The model suggests that the new regulatory environment may have the unintended consequence of inducing banks, especially undercapitalized ones, to invest in riskier assets. This holds both under higher capital requirements (even if risk-based) and under capital-based deposit-insurance premia. Download Paper
A Common Interest game is a game in which there exists a unique vector of payoffs which strictly Pareto-dominates all other payoffs. We consider the undiscounted repeated game obtained by the infinite repetition of such an n-player Common Interest game. We restrict supergame strategies to be computable within Church's thesis, and we introduce computable trembles on these strategies. If the trembles have sufficiently large support, the only equilibrium vector of payoffs which survives is the Pareto-efficient one. The result is driven by the ability of the players to use the early stages of the game to communicate their intention to play cooperatively in the future. The players 'take turns' to reveal their cooperative intentions, and the result is proved by 'backwards induction' on the set of players. We also show that our equilibrium selection result fails when there are a countable infinity of players. Download Paper
Most economists are sympathetic to the idea that concerns for relative position are an important aspect of many economic problems. There has traditionally been a reluctance to include such concerns primarily because models that included them often allow such a broad range of behavior that there are few, if any, restrictions on equilibrium behavior and, hence, such models would have little or no predictive power. In this paper we discuss how reduced form models may naturally give rise to utility functions that depend, in part, on relative standing. There are several advantages of modelling concern for relative standing in reduced form utility functions even when there is no similar concern in the "deep" preferences. It provides structure and constraints on the way that relative standing affects utility, and further, it can yield testable implications about the way that changes in the underlying environment affect the concern for relative standing. We discuss the advantages and disadvantages of modelling social concerns in this way and provide examples that illustrate how concerns for relative standing can affect savings, investment and labor choice decisions. Download Paper
We develop a model of firm size in which firms are unable to access as many consumers as they want. Newly arrived consumers match randomly with firms. Subsequently, consumers must pay search costs to be able to switch firms. This cost promotes an inertial tendency for consumers to remain with the ̄rm they currently buy from. Consequently, established firms enjoy a proprietary relationship with respect to their old customers while new entrants only have access to first time consumers, who are as yet unattached to any firm. As time goes on, firms acquire successive generations of new consumers, and their stock of loyal customers grows gradually. Thus, more senior firms command higher market shares. We construct an industry model based on this hypothesis and show that the aggregate implications of the model are consistent with empirical facts about industry dynamics (e.g., Dunne, Roberts and Samuelson, (1988, 1989) or Davis and Haltiwanger (1992)): Larger and older firms are less likely to exit than younger and smaller firms. In our model this results from the fact that the option value of remaining operative in the aftermath of a high cost-shock is greater for an older firm than for a younger firm because the value of a cost turnaround is greater for the former (which has already accumulated a large customer-base) than for the latter (which has yet to do so). This enables older (and larger) firms to survive adverse cost-shocks which force the exit of younger (and smaller) firms. For similar reasons, R&D expenditures are larger for larger firms, as per the empirical findings surveyed by Cohen and Lewis (1989). Download Paper
This paper examines the effect of competition on firms’ efforts to experiment and learn about market demand. Consumers are assumed to know prices only at sellers they have actually visited, but must bear search costs to find the prices of other sellers. Under these conditions we show that firms’ incentives to experiment are diluted by comparison with the monopoly case and that this effect is stronger the smaller the search cost. The learning environment we portray gives rise to several time paths which have been empirically documented, including penetration pricing, cream-skimming and cyclical pricing. Download Paper
We identify and investigate the basic 'hold-up problem' which arises whenever each party to a contract has to pay some ex-ante cost for the contract to become feasible. We then proceed to show that, under plausible circumstances, a 'contractual solution' to this hold-up problem is not available. This is because a contractual solution to the hold-up problem typically entails writing a 'contract over a contract' which generates a fresh set of ex-ante costs, and hence is associated with a new hold-up problem. Download Paper
In this paper we examine the dynamic resolution of technological adoption in "hardware/software" systems. We are interested in determining to what extent software availability affects hardware sales and/or vice-versa. We first develop a dynamic model for estimating demand when costs (and hence prices) are declining over time. We then estimate it empirically for the case of compact disc players. We ̄find that there is "two-way" feedback between hardware and software for compact disc players. The result that the availability of compatible software (the CDs) plays a significant role in determining the adoption of compact disc players is likely due in part to the fact that compact disc players were not compatible with any existing audio standard. Download Paper