A simple proof of Ekeland and Scheinkman's result on the necessity of a transversality condition

Summary. Ekeland and Scheinkman (1986) prove the necessity of a standard transversality condition under certain technical conditions. Their result is one of the most powerful on the necessity of a transversality condition currently available in the literature, and their proof involves numerous estimations and relies on Ekeland's variational principle and Fatou's lemma. This note relaxes some of their assumptions and provides a simple proof that uses neither Ekeland's principle nor a convergence result like Fatou's lemma. Received: April 24, 1998; revised version: September 8, 1998     

Approximation by finite horizons of the undiscounted one-sector growth model

Summary. In this paper I give a method for finding long-run-average policies in the undiscounted economic growth problem using approximations by finite horizons. Required hypothesis is the strong interiority of T-horizon solutions. Received: March 25, 1996; revised version: July 29, 1997     

A simple proof of the necessity of the transversality condition

Summary. This note provides a simple proof of the necessity of the transversality condition for the differentiable reduced-form model. The proof uses only an elementary perturbation argument without relying on dynamic programming. The proof makes it clear that, contrary to common belief, the necessity of the transversality condition can be shown in a straightforward way. Received: January 22, 2001; revised version: April 2, 2001     

Dynamic labor contracts with temporary layoffs and permanent separations

Summary. We study the implications of optimal dynamic contracts in private information environments for fluctuations in effort and employment across time and productivity states. To this end, we incorporate temporary layoffs and permanent separations as well as on-the-job effort variations into a dynamic model of moral hazard. We consider two different “commitment” environments. In a “full commitment” environment, although the firm can temporarily lay a worker off, neither party can dissolve the contractual relationship once it has been initiated. On the other hand, in a “limited commitment” environment, both parties can dissolve the relationship at the beginning of any period in order to pursue an outside option. We use our model to study the implications of optimal contracts for incentives, employment histories, layoffs and separations across full information, full commitment and limited commitment settings. We compute solutions to the relevant principal-agent problems, endogenously determining the set of states in which separations occur and the domain of the firm's value function, as well as the value function itself. Received: February 28, 2000; revised version: January 21, 2001     

Aggregate fluctuations, financial constraints and risk sharing

Summary. Private information and costly state verification often result in credit rationing in models with smooth investment, affecting both loan size and total investment. The optimal contract is derived in a dynamic stochastic growth model with capital for two types of models: one with symmetric information and the other with asymmetric information and costly state verification. When all information is observed costlessly, the equilibrium optimal contract provides complete insurance to risk-averse savers against aggregate fluctuations. When information is asymmetric and there is costly state verification, the equilibrium optimal contract provides only partial insurance against aggregate shocks. The extent of insurance is measured by the marginal rate of transformation of consumption between borrowers and lenders which is closely linked to the user cost of capital. The deadweight monitoring costs create a wedge between a borrower's cost of capital and a lender's stochastic discount factor, with two results: (i) fluctuations in the user cost of capital provides a mechanism by which aggregate shocks can be␣propagated; (ii) the distribution of capital's share of output among borrowers, lenders, and monitoring costs varies even if capital's share is constant. Capital market frictions not only amplify aggregate fluctuations but also generate cross-sectional fluctuations that may not be observable in aggregate data. Received: November 17, 1997; revised version: April 20, 1998     

Closed-loop equilibrium in a multi-stage innovation race

Summary. We examine a multistage model of an R&D race where players have multiple projects. We also develop perturbation methods for general dynamic games that can be expressed as analytic operators in a Banach space. We apply these perturbation methods to solve races with a small prize. We compute second-order asymptotically valid solutions for equilibrium and socially optimal decisions to determine qualitative properties of equilibrium. We find that innovators invest relatively too much on risky projects. Strategic reactions are ambiguous in general; in particular, a player may increase expenditures as his opponent moves ahead of him. Received: January 3, 2002; revised version: June 14, 2002 RID="*" ID="*" This is the final version of Judd (1985). The author gratefully acknowledges the comments of anonymous referees, Paul Milgrom, seminar participants at Northwestern University, the University of Chicago, the 1984 Summer Meetings of the Econometric Society, University of California at Berkeley, Stanford University, and Yale University, and the financial support of the National Science Foundation (SES-8409786, SES-8606581)     

Recursive structure and equilibria in games with private monitoring

Summary. In each stage of a repeated game with private monitoring, the players receive payoffs and privately observe signals which depend on the players' actions and the state of world. I show that, contrary to a widely held belief, such games admit a recursive structure. More precisely, I construct a representation of the original sequential problem as a sequence of static games with incomplete information. This establishes the ground for a characterization of strategies and, hence, of behavior in interactive-decision settings where private information is present. Finally, the representation is used to give a recursive characterization of the equilibrium payoff set, by means of a multi-player generalization of dynamic programming. Received: February 11, 2002; revised version: July 22, 2002 RID="*" ID="*" I am very grateful to In-Koo Cho, Larry Epstein, Denis Gromb, Stephen Morris, Paolo Siconolfi, Lones Smith and Max Stinchcombe for several insights and suggestions. A referee's comments helped improving the exposition. Finally, I wish to thank the participants to the seminars at MEDS, NYU, Columbia University, Caltech, UCLA, University of Rochester, University of Texas-Austin, Northwestern Summer Microeconomics Conference 98, Summer in Tel Aviv 98, and NASM98.     

Preference for flexibility in infinite horizon problems

Summary. We consider the extension of the classical problem of preference for flexibility to many periods. Preferences are defined over sets of infinite paths of choices. The main result provides a set of axioms on preferences that yield an additive representation over a subjective state space. This space is the set of preferences over choice today and feasible set tomorrow. The main new axiom, stochastic dominance, is a stronger form of the assumption of monotonicity. Received: September 11 2000; revised version: December 18, 2001     

The set of sunspot equilibria in economies with incomplete financial markets: variable asset prices

Summary. I consider the set of equilibria of two-period economies with S extrinsic states of nature in the second period and I assets with linearly independent nominal payoffs. Asset prices are variable. If the number of agents is greater than (S-I), the payoff matrix is in general position and S 2I, the set of equilibrium allocations generically (in utility function space) contains a smooth manifold of dimension (S-1). Moreover, the map from states o f nature to equilibrium allocations (restricted to this manifold) is one-to-one at each equilibrium. Received: February 23, 1998; revised version: June 1, 2000     

Cycles and multiple equilibria in the market for durable lemons

Summary. The paper investigates the nature of market failure in a dynamic version of Akerlof (1970) where identical cohorts of a durable good enter the market over time. In the dynamic model, equilibria with qualitatively different properties emerge. Typically, in equilibria of the dynamic model, sellers with higher quality wait in order to sell and wait more than sellers of lower quality. The main result is that for any distribution of quality there exist an infinite number of cyclical equilibria where all goods are traded within a certain number of periods after entering the market. Received: December 21, 2000; revised version: September 5, 2001     

Saving behavior in stationary equilibrium with random discounting

Summary. We study the implications of random discount rates of future generations for saving behavior and capital holdings in a steady state competitive equilibrium with heterogeneous population. A well-known difficulty in deterministic economies with heterogeneous households is that in steady state only the most patient households hold capital. In this paper we state conditions under which this random discounting is sufficient for households other than the most patient ones to save. We thus provide a simple and natural way of overcoming the aforementioned difficulty. Received: December 28, 1998; revised version: May 19, 1999     

Utility and entropy

Summary. In this paper we study an astonishing similarity between the utility representation problem in economics and the entropy representation problem in thermodynamics. Received: May 17, 1999; revised version: October 16, 2000     

The equivalence of the Dekel–Fudenberg iterative procedure and weakly perfect rationalizability

Summary. Two approaches have been proposed in the literature to refine the rationalizability solution concept: either assuming that a player believes that with small probability her opponents choose strategies that are irrational, or assuming that their is a small amount of payoff uncertainty. We show that both approaches lead to the same refinement if strategy perturbations are made according to the concept of weakly perfect rationalizability, and if there is payoff uncertainty as in Dekel and Fudenberg [J. of Econ. Theory 52 (1990), 243–267]. For both cases, the strategies that survive are obtained by starting with one round of elimination of weakly dominated strategies followed by many rounds of elimination of strictly dominated strategies. Received: 10 December 1998; revised version: 26 April 1999     

Alternating-offer bargaining over menus under incomplete information

Summary. This paper considers bargaining with one-sided private information and alternating offers where an agreement specifies both a transfer and an additional (sorting) variable. Moreover, both sides can propose menus. We show that for a subset of parameters the alternating-offer game has a unique equilibrium where efficient contracts are implemented in the first period. This stands in sharp contrast to the benchmarks of contract theory, where typically only the uninformed side proposes, and bargaining theory, where typically the agreement only specifies a transfer. Received: September 10, 2001; revised version: March 25, 2002 RID="*" ID="*" I benefitted from discussions with Benny Moldovanu, Holger Müller, and Roland Strausz, and from comments made by an anonymous referee.     

我国居民消费偏低的原因和对策研究

近些年来，随着我国经济的快速发展，虽然国民生产总值不断提高，但居民收入增长缓慢，收入差距逐步扩大，整个社会消费倾向偏低，导致消费率偏低。提高消费率有利于解决内需不足引发的一系列问题，提高全国人民的生活水平和质量，为构建和谐社会奠定坚实的基础。     

Contractual restrictions on insider trading: a welfare analysis

Summary. This paper analyzes the welfare effects of permitting firms to negotiate contractually the right to allow corporate insiders to trade shares in the firm on private information. A computational framework is employed to (i) analyze formally the effects of insider trading on managerial investment choice, the informational efficiency of stock prices, and the welfare of all investor types; and (ii) examine the effectiveness of various compensation schemes (such as stock and insider trading rights) to mitigate conflicts of interest between managers and shareholders. I show that shareholders will typically choose not to grant insider trading rights to managers. This decision is socially optimal. Received: September 23, 2000; revised version: December 12, 2000     

Comparing competition and collusion: a numerical approach

Summary. Collusion is a serious problem in many procurement auctions. In this research, I study a model of first price sealed bid procurement auctions with asymmetric bidders. I demonstrate that the equilibrium to the model is unique and describe three algorithms that can be used to compute the inverse equilibrium bid functions. I then use the computational algorithms to compare competitive and collusive bidding. The algorithms are useful for structural estimation of auction models and for assessing the damages from bid-rigging. Received: January 14, 2000; revised version: February 28, 2001     

More on parametric characterizations of risk aversion and prudence

Summary. This note provides an alternative proof for the equivalence of decreasing absolute prudence (DAP) in the expected utility framework and in a two-parametric approach where utility is a function of the mean and the standard deviation. In addition, we elucidate that the equivalence of DAP and the concavity of utility as a function of mean and variance, which was shown to hold for normally distributed stochastics in Lajeri and Nielsen [4], cannot be generalized. Received: November 27, 2000; revised version: November 26, 2001 Correspondence to: T. Eichner     

Core concepts in economies where information is almost complete

Summary. The paper analyzes the properties of cores with differential information, as economies converge to complete information. Two core concepts are investigated: the private core, in which agents' net trades are measurable with respect to agents' private information, and the incentive compatible core, in which coalitions of agents are restricted to incentive compatible allocations. Received: March 15, 2000; revised version: August 24, 2000