Volume 9, Issue 1

Applying techniques developed by Geanakoplos et al. (1989), this paper analyzes the gift exchange between agents with privately observed nonpaternalistic altruism. I find that gift giving between agents under private information of altruism can be analyzed as a conventional signaling game. After applying standard refinements of signaling games, I show that, over nondegenerate ranges of parameter values, private information introduces systematic biases in agents' behavior. First, agents tend to give larger gifts than under full information. Second, despite that fact that agents have no intrinsic concern for reciprocity or fairness, the more altruistic the recipient is, the more the donor exaggerates the gift size. The second finding gives rise to a new theory of reciprocity according to which private information of unconditional altruism can lead to reciprocal behavior.

One of the best known ideas in the study of bounded rationality is Simon's satisficing; yet we still lack a standard formalization of the heuristic and its implications. We propose a mathematical model of satisficing which explicitly represents agents' aspirations and which explores both single-person and multi-player contexts. The model shows that satisficing has a signature performance-profile in both contexts: (1) it can induce optimal long-run behavior in one class of problems but not in the complementary class; and (2) in the latter, it generates behavior that is sensible but not optimal. The model also yields empirically testable predictions: in certain bandit-problems it pins down the limiting probabilities of each arm's use, and it provides an ordering of the arms' dynamical use-probabilities as well.

We study the optimal auction problem with participation costs in the symmetric independent private values setting, where bidders know their valuations when they make independent participation decisions. After characterizing the optimal auction in terms of participation cutoffs, we provide an example where it is asymmetric. We then investigate when the optimal auction will be symmetric/asymmetric and the nature of possible asymmetries. We also show that, under some conditions, the seller obtains her maximal profit in an (asymmetric) equilibrium of an anonymous second price auction. In general, the seller can also use non-anonymous auctions that resemble the ones that are actually observed in practice.

I generalize Gul and Pesendorfer's (2001) model of temptation to a multi-period framework where preferences are defined over menus of menus rather than over menus of terminal consumptions. This extension can be applied to model preemptive temptations, self-deception, and biased perceptions of subjective uncertainty.

This paper considers a simple adaptive learning rule in Bayesian games with binary actions where players employ threshold strategies. Global convergence results are given for supermodular games and potential games. If there is a unique equilibrium, players' strategies converge almost surely to it. Even if there is not, in potential games and in the two-player case in supermodular games, any limit point of the learning process must be an equilibrium. In particular, if equilibria are isolated, the learning process converges to one of them almost surely.

While a key function of contracts is to provide incentives, the incentives of judges to enforce the terms of a contract have rarely been examined. This paper develops a simple model of judicial agency in which judges are corrupt and can be bribed by contracting parties. Higher-powered contracts expose contracting parties to more frequent and more severe corruption, which in turn lessens the incentives actually provided by the contract. Consequently the model predicts that individuals will commonly refrain from writing high-powered contracts, even when such contracts would be valuable absent judicial agency. I show that similar implications can also be obtained by considering other forms of imperfection in contract enforcement, such as variable expenditures on legal representation. I use the model to develop implications for the optimal punishment of individuals who are extorted by corrupt judges, and to establish circumstances under which a right-of-appeal is optimal.

Dynamic consistency leads to Bayesian updating under expected utility. We ask what it implies for the updating of more general preferences. In this paper, we characterize dynamically consistent update rules for preference models satisfying ambiguity aversion. This characterization extends to regret-based models as well. As applications of our general result, we characterize dynamically consistent updating for two important models of ambiguity averse preferences: the ambiguity averse smooth ambiguity preferences (Klibanoff, Marinacci and Mukerji [Econometrica 73 2005, pp. 1849-1892]) and the variational preferences (Maccheroni, Marinacci and Rustichini [Econometrica 74 2006, pp. 1447-1498]). The latter includes max-min expected utility (Gilboa and Schmeidler [Journal of Mathematical Economics 18 1989, pp. 141-153]) and the multiplier preferences of Hansen and Sargent [American Economic Review 91(2) 2001, pp. 60-66] as special cases. For smooth ambiguity preferences, we also identify a simple rule that is shown to be the unique dynamically consistent rule among a large class of rules that may be expressed as reweightings of the Bayes' rule.

There is a widespread belief that in auctions with private values, the seller's revenue is increasing in the number of bidders. We show that there exists an auction setting with symmetric and affiliated private values in which the seller's expected revenue in a first price auction is decreasing in the number of bidders who participate in the auction.

In this paper we study the optimal file-sharing mechanism in a peer-to-peer network with a mechanism design perspective. This mechanism improves upon existing incentive schemes. In particular, we show that peer-approved scheme is never optimal and service-quality scheme is optimal only under certain circumstances. Moreover, we find that the optimal mechanism can be implemented by a mixture of peer-approved and service-quality schemes.

It is often assumed (for analytical convenience, but also in accordance with common intuition) that consumer preferences are convex. In this paper, we consider circumstances under which such preferences are (or are not) optimal. In particular, we investigate a setting in which goods possess some hidden quality with known distribution, and the consumer chooses a bundle of goods that maximizes the probability that he receives some threshold level of this quality. We show that if the threshold is small relative to consumption levels, preferences will tend to be convex; whereas the opposite holds if the threshold is large. Our theory helps explain a broad spectrum of economic behavior (including, in particular, certain common commercial advertising strategies), suggesting that sensitivity to information about thresholds is deeply rooted in human psychology.

Many goods have network externalities. When the number of agents possessing such goods is small, the agents may not gain sufficient utility from the goods. Agents then have an incentive to delay their purchasing decisions. Such delays have negative effects on the agents' utility, so equilibrium with delays is inefficient. We propose a method of resolving this problem using a two-step scheme with participation fees and subsidies. If this method is used, and certain conditions are satisfied, all agents purchase the good and the delay in equilibrium decreases.

The paper develops a simple theory of segmentation and fee-setting in certification markets. The basis for the theory is that certifiers offer differentiated tests; for a given object it is more difficult to pass the test of certifier i than the test of certifier j. Given the test standards, certifiers compete for customers via their fee-setting. Segmentation occurs in equilibrium: sellers with low unobservable quality self-select to an easy test and sellers with high unobservable quality self-select to a hard test. Moreover, sellers choosing an easy test pay a lower (endogenous) certification fee than sellers choosing a hard test. These results are consistent with evidence from the market for auditors and other markets, not readily explained by existing theories.

In economics the main efficiency criterion is that of Pareto-optimality. For problems of distributing a social endowment a central notion of fairness is no-envy (each agent should receive a bundle at least as good, according to her own preferences, as any of the other agent's bundle). For most economies there are multiple allocations satisfying these two properties. We provide a procedure, based on distributional implications of these two properties, which selects a single allocation which is Pareto-optimal and satisfies no-envy in two-agent exchange economies. There is no straightforward generalization of our procedure to more than two-agents.

This paper investigates how interest rates on liquid assets and excess returns on risky assets are determined when only safe assets can be used as liquid assets when waiting for an informative signal of future payoffs. In particular, we carefully differentiate between a demand for liquid assets while waiting for new information and a demand for safe assets for precautionary reasons. Employing Kreps--Porteus preferences, numerical examples demonstrate that larger waiting-options premiums (lower interest rates) emerge with higher risk aversion in combination with more elastic intertemporal substitution.

The paper studies asset prices and capital accumulation in a monetary economy with non-diversifiable idiosyncratic risks. A government issued unbacked currency is introduced into agent's preferences in a dynamic GEI (General Equilibrium with Incomplete market) model with CARA preferences and normal disturbances. Closed form expressions for equilibrium allocations and prices are derived. The paper identifies two new channels through which money growth affects self insurance, interest rate and capital accumulation. The paper also shows that the resulting non-linearities in the relationships between the rate of inflation, the steady state capital stock and the interest rate, may even cause an optimal rate of inflation not to exist. Further, the Friedman rule is shown to be suboptimal for some economies.

Consider a Cournot oligopoly where producers launch new products. At first potential buyers are unaware of the product, and firms decide on levels of production, advertising expenditure and a cost-reducing investment. We find the conditions for complementarities among scale, advertising and innovation strategies to arise. In a duopoly with substitute products all variables are higher for the firm that moves from mass advertising to targeted advertising but decrease for the other. In an oligopoly with complementary products all variables are higher for all firms when they shift away from mass marketing. We conclude by linking our results to the empirical literature on internalization which finds a positive relationship between advertising intensity and foreign direct investment.

This paper develops a microeconomic model of directed search, where firms are heterogeneous in the number of vacancies advertised, and wages affect workers' choices when both applying for jobs and accepting a job. An aggregate matching function is derived, which incorporates workers' preferences for firms. The aggregate level of matches is shown to be independent of the workers' preferences in the job acceptance stage. When firms' labor demands are heterogeneous, the matching market equilibrium outcome is suboptimal. Matching efficiency is, however, attained in equilibrium, when wages are employed as a rationing device. This results in wage dispersion, despite workers being homogeneous.

In a modified version of Rubinstein's bargaining game, two players expect the random arrival of a third party, from whom one of them will receive an interim disagreement payoff in every period until an agreement is finally reached. Each player thinks that his own probability of receiving the disagreement payoff is greater than that assessed by the other player; that is, they are mutually optimistic. We show that when the level of optimism is high and not very durable, equilibrium agreement is delayed until the uncertainty is fully resolved. The efficiency loss caused by such a delay remains substantial when the players are extremely patient.

We adopt the Shapley value approach to examine the fair allocation of the depreciation charges among the time periods of the asset's useful life. Essentially, the allocation under the Shapley value solution rewards each time period of the asset's useful life with a share of the earnings that corresponds to its "responsibility" in the earnings-generating process. The latter is thus consistent with the developments in accounting standards, which maintain that the depreciation and amortization methods should reflect the pattern in which the asset's economic benefits are consumed by the enterprise. We show that the Shapley solution always conforms to a set of fundamental accounting requirements such as the matching principle and the impairment test. Moreover, unless the asset is associated with constant revenues and/or extremely profitable investments, the Shapley value solution can never coincide with the prevalent straight-line depreciation method. Finally, we identify the family of earnings patterns for which the Shapley solution coincides with the equal surplus and the economic depreciation methods.

We discuss how efficiently a unit tax deals with external damage problems when economies of scale characterize a monopolistically competitive market in which consumers' value product variety. It turns out that neither the number of varieties nor the quantity of each variety is at the optimum under a unit tax. Moreover, aggregate production costs are not minimized under a unit tax. For practical policy purposes, some results suggest that a Pigouvian tax can replace a tax taking into account monopoly. Our findings make this conclusion false when the number of firms is endogenous.

The relationship between competition and performance–related pay has been analyzed in single–principal–single–agent models. While this approach yields good predictions for managerial pay schemes, the predictions fail to apply for employees at lower tiers of a firm's hierarchy. This paper describes a principal multi-agent model of incentive pay that analyzes the effect of changes in the competitiveness of markets on lower tier incentive payment schemes. The results explain why the payment schemes of agents located at low and mid tiers are less sensitive to changes in competition when aggregated firm data is used.

This paper considers a vertical differentiation model with positive network effects. It is based on the assumption that consumers belong to the same network if they buy products exhibiting close characteristics. Thus, the network has two characteristics: its intensity and its selectivity. The higher the network intensity, the more positively affected the consumer is by the network size. The network selectivity corresponds to how close the products' characteristics should be to be perceived by consumers as compatible. The closer two compatible products are in the product space, the more selective the network.We analyze the strategic behavior in terms of prices and qualities of two firms: an incumbent and a potential entrant. By choosing its quality the entrant chooses at the same time to be compatible or not.We show that if the network intensity is moderate, it is always profitable for the entrant to enter the market. In this case the entrant is compatible with the incumbent when the network is not very selective and is incompatible when the network is selective. If the network intensity is strong, we prove that it acts as a barrier to entry under incompatibility. The equilibrium outcomes in this case are either no entry or compatible.

This paper investigates mixed strategy equilibria in a capacity-constrained price competition among three firms. It is shown that the equilibria in an asymmetric oligopoly are substantially different from those in a duopoly and symmetric oligopoly. In an asymmetric triopoly, it is possible that (i) a continuum of equilibria exists and that (ii) the lowest price of the smallest firm is higher than that of the others and the smallest firm earns more than the max-min profit in undominated strategies. In particular, the second finding sheds light on a new pricing incentive in Bertrand competitions. As an application, the equilibrium characterizations give rise to a new class of merger paradoxes.

For a symmetric two-stage game, where firms first choose capacities, then compete in prices, Kreps and Scheinkman (Bell Journal of Economics, 1983, 14(2), pp. 326-337) prove that under efficient rationing the Nash equilibrium coincides with the Cournot equilibrium. We extend the model to include asymmetric costs and provide new results showing that the capacity choice game is dominance-solvable, just like the Cournot game. Further, we provide a simple sufficient condition, under which the dominance-solvable result extends to proportional rationing. The results provide new insights into the robustness of Cournot coincidence under alternate demand rationing schemes.

Using up to nine different ways to represent homogeneous technologies with decreasing returns to scale, this article presents and proves identities between those different representations of such technologies, outlining the homogeneity properties of each representation. These identities, which allow to shift from one representation of a technology to another -- and which are summarized in a matrix of identities -- can be useful since they provide a tool to obtain explicit functional forms for homogeneous technologies. They can also be useful to simplify computational procedures when different representations of a technology are needed. Finally, the article also refers explicitly to some aspects of producer theory that are often neglected or treated in a marginal way in the literature, such as the inverse supply, the non conditional cost and the inverse input demands functions.

This paper analyzes the delegation of contracting capacity in a moral hazard environment with sequential production in a project which involves a principal and two agents. The agent in charge of the final production can obtain soft information about the other agent's effort choice by investing in monitoring. I investigate the circumstances under which it is optimal for the principal to use a centralized organization in which she designs the contracts with both agents or to use a decentralized organization in which she contracts with only one agent, and delegates the power to contract with the other agent. It is shown that in this setting a decentralized organization can be superior to a centralized organization. This is because the principal is better off under monitoring and the incentives for an agent to invest in monitoring can be higher in a decentralized organization. The circumstances under which this is true are related to monitoring costs and the importance of each agent for production. The results explain the recent application of the design-build method in public procurement.

Traditional trade theory maintains that international economic integration always yields potential welfare benefits. This result can however be maintained only in a world bereft of its institutional and cultural dimensions. In this paper we show that, once institutional factors are introduced, integration may be detrimental to welfare. Exploiting a game theoretical approach, we consider the integration between two societies that only differ in their institutional structures. Two important results are derived. First, intercommunity integration may trigger the demise of the erstwhile internal arrangements. Second, the collapse of the domestic institutional equilibrium can lead to a loss of welfare for the community as a whole.

A regulator imposes a universal service obligation (USO) on a vertically integrated firm that owns an essential network. The regulator has imperfect information about the network's fixed cost. Network access is provided to licensed competitors. The USO consists in a constraint on market coverage and is compensated through a mix of public funds and transfers from entrants. We first use a basic adverse selection model to show that, because of informational rents, a sufficiently high shadow cost of public funds can lead to a lower coverage with the USO than without it. We then show that this result tends to be robust in various realistic extensions of the basic model.

Using a theoretical model of political competition between two candidates who could differ in their (unverifiable) ability to produce public good, popularity, and ethics, I study the effectiveness of three commonly discussed anti-corruption reforms (higher salaries, higher penalties, and constitutional constraints on fiscal policy). In the model, each candidate proposes an income tax rate and a public good level. The difference between the collected taxes and the cost of public good is stolen by the elected politician. The voting decision is probabilistic. I show that under certain conditions each reform could increase the level of corruption or reduce the voter's welfare through other channels.

We study a general class of pure exchange economies that have multiple equilibria. This class generalizes an example presented by Shapley and Shubik. For such economies, we find easily verified conditions that determine whether there are multiple equilibria. We also provide simple methods for constructing economies in which arbitrary pre-specified sets of prices are equilibria. These economies have strong comparative statics properties, since prices at interior competitive equilibrium depend on the parameters of utility but not on the endowment quantities. We believe that this easily manipulated special case is a valuable addition to the class of simple general equilibrium economies that can be used as testing grounds in economic theory.

Building upon recent work of Gintis, we study evolutionary dynamics in an economy with Leontieff preferences and corner endowments for which the equilibrium is completely indeterminate. We exhibit a class of dynamics which selects, via stochastic stability, the equilibrium minimizing the quantities traded.

This paper models two discontinuities that have been claimed to constitute important exceptions to the standard economic theory of human motivation. The first is a discontinuity in the distribution across population types of the willingness to accept payment in return for certain services such as giving blood, because such services given free are more worthwhile than when performed for payment. The second is that people who give services free may refuse to sell them for some positive price (this is known as crowding out). The paper models both phenomena when individuals act to signal their type in a two-period game with assortative matching. The former is the unique equilibrium of a signaling game in which individuals announce the prices at which they will perform a civic action. The latter may be observed as one of two equilibria of a screening game in which individuals have only a binary participation decision available to signal their type.

This paper presents a tractable model that allows us to study career concerns when the strength of a worker's incentives depends on his employment history. More specifically, the paper incorporates standard job assignments into the main model in Holmstrom (1999). Equilibrium wages, equilibrium job assignments, and the strength of career-concern incentives are the same for all employment histories that lead to the same worker's reputation. (With reputation we refer to beliefs about the worker's future productivity.) We show that, typically, workers with better reputation have stronger incentives than workers with worse reputation. Furthermore, we show that when the strength of incentives depends on employment history, (i) a ratchet effect may appear, (ii) in spite of this ratchet effect, incentives may be stronger, and (iii) incentives may be stronger when beliefs about ability are more precise.

In the present paper stationary pure-exchange overlapping generations economies with L goods per date and M consumers per generation are considered. It is shown that for an open and dense set of utility functions there exist endowment vectors such that N-cycles exist for N less than or equal to L+1 and L less than or equal to M. The approach to existence of endogenous fluctuations is basic in the sense that the prime ingredients are the implicit function theorem and linear algebra. Moreover it is sketched how the approach can be applied to show that for an open and dense set of utility functions there exist endowment vectors such that sunspot equilibria, where prices at every date only depends on the state at that date, exist.

This paper analyses principal-agent contracts when the risk-averse agent's action generates information that is not directly verifiable but is used to make a risky decision in a formulation more general than previously studied. It focuses on the impact on the decision made and the contract used, establishing a necessary and sufficient condition for the principal to gain by distorting decisions away from what is efficient and conditions under which there is no conflict between incentives to make decisions and to take action. Applications to investing in a risky project and bidding to supply a good or service illustrate those results.

We consider the sale of an asset via sequential search over a finite time horizon and analyze the problem in both the posted price and the reservation price regimes. The distinguishing feature of this search model is the fact that the asset deteriorates with the passage of time. Under mild conditions, we show that the seller's optimal posted price (and the seller's optimal reservation price) per remaining unit of the asset decreases as time passes.

This paper studies the aspiration-based learning dynamics in symmetric normal-form games played at multiple locations. In particular, the aspiration level in one location is linked to the average performances of players in observable locations. With a decentralized information structure, the learning dynamics converge to limit states. For a large class of information structures and games, when there exists trembles in the updating of aspiration levels, the unique stochastically stable equilibrium is characterized by the Pareto efficient symmetric outcome. In the prisoners' dilemma, if the probability of trembles is sufficiently small, both players in every location will ultimately cooperate most of the time.

We explore the consequences of electoral competition for nonlinear income taxation. Our model is a dynamic version of the standard two-party electoral competition model adapted to nonlinear income taxation. The theory has a number of desirable features. First, equilibria always exist, even though the set of admissible tax policies is multidimensional. Second, the Nash set can be characterized generically, and its components give sharp predictions. Third, the features of equilibrium tax policies depend only on empirically meaningful fundamentals.Equilibrium tax schedules benefit the more numerous income groups and place the burden of taxation on income groups with fewer voters. For empirical income distributions, the features of an equilibrium tax schedule are reminiscent of Director's law of public income redistribution (Stigler [39]).

We utilize the analytical construct of a stochastic supply function to provide an aggregate representation of a finite collection of standard deterministic supply functions. We introduce a consistency postulate for a stochastic supply function that may be satisfied even if no underlying deterministic supply function is rationalizable in terms of profit maximization. Our consistency postulate is nonetheless equivalent to a stochastic expansion of supply inequality, which summarizes the predictive content of the traditional theory of competitive supply. A number of key results in the deterministic theory follow as special cases from this equivalence. In particular, it yields a probabilistic version of the law of supply, which implies the traditional specification. Our analysis thus provides a necessary and sufficient axiomatic foundation for a de-coupling of the predictive content of the classical theory of competitive firm behavior from its a priori roots in profit maximization, while subsuming the traditional theory as a special case.

I present a stochastic version of Tirole's (1996) collective reputation model. In equilibrium, group behavior is persistent due to complementarity between the current incentives of group members and the group's reputation, which depends on its history. A group can maintain a strong reputation even as conditions become unfavorable, but an improvement in the environment may not help a group with a poor reputation. I also connect the model to the theory of statistical discrimination and show that the same mechanism can explain why discrimination might persist over time.

Networks of social and economic interactions are often influenced by unobserved structures among the nodes. Based on a simple model of how an unobserved community structure generates networks of interactions, we axiomatize a method of detecting the latent community structures from network data. The method is based on maximum likelihood estimation.

This paper explores how income distribution affects market structure, prices, and economic well-being of different consumer groups. I consider a general equilibrium model of monopolistic competition with free entry, heterogenous firms and consumers that share identical but non-homothetic preferences. The results in the paper suggest that poverty reduction might be of a greater importance than lowering income inequality, as lower income inequality does not necessarily lead to welfare gains of the poor. In particular, I show that higher income inequality may benefit the poor via a trickle-down effect operating through the entry of firms into the market.

We consider an allotted procurement contract awarded by means of a combinatorial first-price sealed-bid auction. Two small firms and a larger firm are competing. Each small firm is interested in a single lot whereas the large firm transmits a global offer. Under a specific informational framework, we derive the asymmetric combinatorial equilibrium bidding strategies and show that they exhibit a free-riding effect. We show that this effect is increasing with the level of uncertainty and decreasing with risk aversion. When all the firms are risk neutral or equally risk averse, the magnitude of the free-riding effect is unaffected by the division of the contract chosen by the public buyer. Nevertheless, when each firm exhibits its own risk aversion parameter, we find that the free-riding effect is reduced (resp. increased) as the more risk averse small firm competes for a larger (resp. smaller) part of the contract.

This paper characterizes the behavior of value functions in dynamic stochastic discounted programming models near fixed points of the state space. When the second derivative of the flow payoff function is bounded, the value function is proportional to a linear function plus geometric term. A specific formula for the exponent of this geometric term is provided. This exponent continuously falls in the rate of patience.If the state variable is a martingale, the second derivative of the value function is unbounded. If the state variable is instead a strict local submartingale, then the same holds for the first derivative of the value function. Thus, the proposed approximation is more accurate than Taylor series approximation.The approximation result is used to characterize locally optimal policies in several fundamental economic problems.

I study sequential second price auctions with multi-unit demands in a complete information setting, focusing on cases in which payoffs are non-separable as a consequence of decreasing marginal values. At the equilibrium outcome a buyer behaves as a monopsonist with respect to the residual supply, which raises the possibility of inefficiency. Moreover, I construct an equilibrium that exhibits declining prices, a fact that has been empirically observed.