On coalitional stability of anonymous interim mechanisms

Summary.   In a situation where agents have private information, we investigate the stability of mechanisms with respect to coalitional deviations. In the cooperative tradition, we first extend the notion of Core, taking into account the information a coalition may have when it forms and the conjectures of outsiders. This leads us to propose a family of Cores rather than a single one. Secondly, we study the stability of Core mechanisms to secession proposals in simple noncooperative games. The two different stability analyses, normative and strategic, tend to give support to the more natural extension of the Core, called Statistical Core, only in situations where some strong form of increasing returns to coalition is met. Without this property, arguments for a concept of Core that is non empty in a reasonably large class of problems are less compelling. Applications to taxation and insurance are given. Received: September 6, 1999; revised version: December 3, 1999     

A simple axiomatization and constructive representation proof for choquet expected utility

>P>Summary. We provide a set of simple and intuitive set of axioms that allow for a direct and constructive proof of the Choquet Expected Utility representation for decision making under uncertainty. Received: October 29, 2002; revised version: November 13, 2002 RID="*" ID="*" We thank Matthew Ryan for very useful comments and suggestions on related work and for encouraging us to write this note. Correspondence to: S. Grant     

Uncertainty and entry deterrence

Summary. We study a model where capacity installation by an incumbent firm serves to deter others from entering the industry. We argue that uncertainty about demand or costs forces the incumbent to choose a higher capacity level than it would under certainty. This higher level diminishes the attractiveness of deterrence (Proposition 1) and, therefore, the range of parameter values for which deterrence occurs (Proposition 2). Received: July 10, 1997; revised version: November 21, 1997     

Incentive compatible core and competitive equilibria in differential information economies

Summary. If the allocations of a differential information economy are defined as incentive compatible state-contingent lotteries over consumption goods, competitive equilibrium allocations exist and belong to the (ex ante incentive) core. Furthermore, any competitive equilibrium allocation can be viewed as an element of the core of the n-fold replicated economy, for every n. The converse holds under the further assumption of independent private values but not in general, as shown by a counter-example. Received: August 9, 1999; revised version: September 12, 1999     

Strategic transmission of information and short-term commitment

Summary. We examine the strategic role of information transmission in a repeated principal-agent relationship where the agent produces information that is useful to the principal. The agent values continuous employment for the principal because he makes a relationship-specific investment that can yield rents to him when the relationship is renewed. Assuming that the parties are sufficiently impatient, we show that full disclosure of the information produced occurs early in the relationship when the principal can commit to a long-term relationship, when the agent observes his valuation of continuous employment after making a report on information produced, or when the agent obtains a low valuation of continuous employment before making a report. By contrast, a strategic delay in the transmission of information occurs when the principal can only commit to a short-term relationship and the agent obtains a high valuation of continuous employment before making a report. Received: October 15, 1997; revised version: July 27, 1998     

Capacity constrained firms in (labor) markets with adverse selection

Summary. We discuss a competitive (labor) market where firms face capacity constraints and individuals differ according to their productivity. Firms offer two-dimensional contracts like wage and task level. Then workers choose firms and contracts. Workers might be rationed if the number of applicants exceeds the capacity of the firm. We show that under reasonable assumptions on the distribution of capacity an equilibrium in pure strategies (by the firms) exists. This result stands in contrast to the case of unlimited capacity. The utility level is uniquely determined in equilibrium. No rationing occurs in equilibrium, but it does off the equilibrium path. Received: December 29, 1999; revised version: November 30, 2000     

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     

Incentives in market games with asymmetric information: the core

Summary. This paper examines the ex ante core of a pure exchange economy with asymmetric information in which state-dependent allocations are required to satisfy incentive compatibility. This restriction on players' strategies in the cooperative game can be interpreted as incomplete contracts or partial commitment. An example is provided in which the incentive compatible core with nontransferable utility is empty; the game fails to be balanced because convex combinations of incentive compatible net trades can violate incentive compatibility. However, randomization of such strategies leads to ex post allocations which satisfy incentive compatibility and are feasible on average. Hence, convexity is preserved in such a model and the resulting cooperative games are balanced. In this framework, an incentive compatible core concept is defined for NTU games derived from economies with asymmetric information. The main result is nonemptiness of the incentive compatible core. Received: December 26, 2001; revised version: June 11, 2002 RID="*" ID"*" This work was financed, in part, by contract No 26 of the programme “P?le d'attraction interuniversitaire” of the Belgian government, and, in part, by research grant SBR93-09854 from the U.S. National Science Foundation. Much of my thinking about this topic was developed during a wonderful visit to CORE for the 1991–1992 academic year (on sabbatical from the University of Pennsylvania). This paper was originally circulated in December 1991 as CARESS Working Paper #91-38, Center for Analytic Research in Economics and the Social Sciences, Department of Economics, University of Pennsylvania and in February 1992 as CORE Discussion Paper 9221, Center for Operations Research and Econometrics, Université Catholique de Louvain, Louvain-la-Neuve, Belgium. RID="*" ID="*" At the very start of my research, Jean-Fran?ois Mertens was almost a co-author. Fran?ois Forges provided detailed comments at a later stage, during my visit to THEMA, Université Cergy-Pontoise, in Spring 1997. They are entitled to the customary disclaimer.     

Diversification, convex preferences and non-empty core in the Choquet expected utility model

Summary. We show, in the Choquet expected utility model, that preference for diversification, that is, convex preferences, is equivalent to a concave utility index and a convex capacity. We then introduce a weaker notion of diversification, namely “sure diversification.” We show that this implies that the core of the capacity is non-empty. The converse holds under concavity of the utility index, which is itself equivalent to the notion of comonotone diversification, that we introduce. In an Anscombe-Aumann setting, preference for diversification is equivalent to convexity of the capacity and preference for sure diversification is equivalent to non-empty core. In the expected utility model, all these notions of diversification are equivalent and are represented by the concavity of the utility index. Received: July 27, 1999; revised version: November 7, 2000     

Incentive compatible contractible information

Summary. The paper seeks to characterize what information is always available for contracting, independent of the form of the contract and the probabilities of different states of nature. The paper denotes such information as contractible. It is established that it is possible to speak uniquely of maximal contractible information. Several characterizations are exhibited. In particular, it is shown that if either (a) punishments are bounded everywhere, or (b) deviations from truth-telling are either always or never detected, then maximum contractible information coincides with where is the information partition of agent j. An argument is given for why (b) may be expected to hold. Received: August 7, 2000; revised version: December 21, 2001 RID="*" ID="*" I thank Michael Chwe, Douglas Diamond, Lars Stole, Robert Townsend, Nicholas Yannelis and an anonymous referee for helpful comments.     

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     

Capacity precommitment as a barrier to entry: A Bertrand-Edgeworth approach

Summary. With few exceptions, the literature on the role of capacity as a strategic entry deterrent has assumed Cournot competition in the post-entry game. In contrast, this paper studies a model in which the incumbent and entrant sequentially precommit to capacity levels before competing in price. Interesting deterrence effects arise because firms need time to build, that is, cannot adjust capacity instantaneously in the post-entry game. This approach produces a simple and intuitive set of equilibrium behaviors and generates clear predictions about when these different outcomes are likely to arise. Our model also departs substantially from the existing literature in concluding that sunkness of capacity costs is neither necessary nor sufficient for capacity to have precommitment value. Received: August 25, 1999; revised version: October 15, 1999     

Existence of equilibrium in an OLG model with production and altruistic preferences

Summary. This note deals with the existence and uniqueness of a non-trivial steady-state equilibrium in an overlapping generations (OLG) model with productive capital and altruistic agents. We establish a necessary and sufficient condition for operative bequests which extends Abel (1987) and Weil (1987). Interestingly, we prove that the OLG model with production and altruistic agents always experiences a non-trivial steady-state equilibrium. Received: July 16, 1998; revised version: January 29, 1999     

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     

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     

Probability of survival in a random exchange economy with dependent agents

Summary. In this paper I analyze the general equilibrium in a random Walrasian economy. Dependence among agents is introduced in the form of dependency neighborhoods. Under the uncertainty, an agent may fail to survive due to a meager endowment in a particular state (direct effect), as well as due to unfavorable equilibrium price system at which the value of the endowment falls short of the minimum needed for survival (indirect terms-of-trade effect). To illustrate the main result I compute the stochastic limit of equilibrium price and probability of survival of an agent in a large Cobb-Douglas economy. Received June 7, 2001; revised version: January 7, 2002 RID="*" ID="*" I would like to thank Mukul Majumdar and Thomas DiCiccio for helpful discussion and an anonymous referee for valuable comments and suggestions.     

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     

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.     

Disaggregation of excess demand and comparative statics with incomplete markets and nominal assets

Summary. We prove that locally, Walras' law and homogeneity characterize the structure of market excess demand functions when financial markets are incomplete and assets' returns are nominal. The method of proof is substantially different from all existing arguments as the properties of individual demand are also different. We show that this result has important implications and is part of a more general result that excess demand is an essentially arbitrary function not just of prices, but also of the exogenous parameters of the economy as asset returns, preferences, and endowments. Thus locally the equilibrium manifold, relating equilibrium prices to these parameters has also no structure. Received: September 17, 1996; revised version: November 7, 1997