The type-agent core for exchange economies with asymmetric information

The type-agent core is a new solution concept for exchange economies with asymmetric information. It coincides with the set of subgame-perfect equilibrium outcomes of a simple competitive screening game. Uninformed intermediaries help the agents to cooperate in an attempt to make some profit. The paper extends the work of Perez-Castrillo [Cooperative outcomes through non-cooperative games, Games Econ. Behav. 7 (1994) 428-440] to exchange economies with non-transferable utility and asymmetric information. The type-agent core is a subset of Wilson's coarse core [Wilson, Information, efficiency, and the core of an economy, Econometrica 46 (1978) 807-816]. It is never empty, even though it may be a strict subset of Wilson's fine core. In addition, it converges towards the set of constrained market equilibria as the economy is replicated.     

A two-stage core with applications to asset market and differential information economies

Summary. We introduce a new core concept, called the two-stage core, which is appropriate for economies with sequential trade. We prove a general existence theorem and present two applications of the two-stage core: (i) In asset markets economies where we extend our existence proof to the case of consumption sets with no lower bound, in order to capture the case of arbitrary short sales of assets. Further, we show that the two-stage core is non empty in the Hart (1975) example where a rational expectations equilibrium fails to exist. (ii) In differential information economies where we provide sufficient conditions for the incentive compatibility of trades. Namely, that no coalition of agents can misreport the true state and provide improvements to all its members, even by redistributing the benefits from misreporting. Received: December 20, 1995; revised version: December 6, 1996     

Economies with price-dependent preferences

With the exception of existence, not much is known of economies where individual preferences may depend on prices. We show that the main properties of competitive equilibria that fall under the general heading of qualitative comparative statics remain true when preferences are price-dependent, provided that the total resources are allowed to vary in the parameter space. The equilibrium set is a smooth manifold diffeomorphic to a Euclidean space; the natural projection is a smooth proper map, with topological degree one; equilibria always exist, and are locally unique for an open and dense set of economies.     

General equilibrium in economies with adverse selection

We model economies of adverse selection as Arrow–Debreu economies. In the spirit of Prescott and Townsend (Econometrica 52(1), 21–45, 1984a), we identify the consumption set of the individuals with the set of lotteries over net transfers. Thus, prices are linear in lotteries, but they may be non linear in commodity bundles. First, we study a weak equilibrium notion by viewing the economy of adverse selection as a pure exchange economy. The weak equilibrium set is non empty, but some of the allocations may be inefficient, and the equilibria indeterminate. Second, following Prescott and Townsend (Econometrica 52(1), 21–45, 1984a), we introduce an intermediary (firm) supplying feasible and incentive compatible measures. Equilibria are constrained efficient, but the equilibrium set is empty for an open set of economies containing the Rothschild and Stiglitz insurance economies. The research of A. Rustichini was supported by the NSF grant NSF/SES-0136556.     

Determinacy of competitive equilibria in economies with many commodities

This paper provides a framework for establishing the determinacy of equilibria in general equilibrium models with infinitely many commodities and a finite number of consumers and producers. This paper defines a notion of regular economy for such models and gives sufficient conditions on the excess savings equations characterizing equilibria under which regular economies have a finite number of equilibria, each of which is locally stable with respect to perturbations in exogenous parameters, and under which regular economies are generic. This paper also defines two notions of concavity, called uniform concavity and weighted uniform concavity, which generalize standard finite-dimensional notions of differential concavity to an infinite-dimensional setting by prohibiting goods from becoming perfect substitutes asymptotically. For the case of economies in which there are countably many commodities, such as discrete time models or markets with countably many assets, results in this paper show that equilibria are generically determinate as long as utility functions and production sets are uniformly concave or weighted uniformly concave. Received: November 7, 1996; revised version: March 13, 1998     

Rational expectations equilibria of economies with local interactions

We consider general economies in which rational agents interact locally. The local aspect of the interactions is designed to represent in a simple abstract way social interactions, that is, socioeconomic environments in which markets do not mediate all of agents’ choices, which might be in part determined, for instance, by family, peer group, or ethnic group effects. We study static as well as dynamic infinite horizon economies; we allow for economies with incomplete information, and we consider jointly global and local interactions, to integrate e.g., global externalities and markets with peer and group effects. We provide conditions under which such economies have rational expectations equilibria. We illustrate the effects of local interactions when agents are rational by studying in detail the equilibrium properties of a simple economy with quadratic preferences which captures, in turn, local preferences for conformity, habit persistence, and preferences for status or adherence to aggregate norms of behavior.     

Options and sunspots in a simple monetary economy

Summary. We study sunspot immunity in a dynamic monetary economy in which consumers are allowed to trade put and call option contracts on the general price level. We define the concept of strong sunspot immunity to characterize economies that have no sunspot equilibria regardless of the number of extrinsic states and their probabilities of occurrence. We show that a small number of option contracts can make an economy strongly sunspot immune. In addition, we demonstrate how asset re-trading opportunities, and the associated capital gains and losses, reduce the number of options needed for this result to obtain. Received: August 13, 1996; revised version: January 20, 1997     

FARSIGHTED COALITIONAL STABILITY OF A PRICE LEADERSHIP CARTEL

This paper analyzes the farsighted behaviour of firms that form a dominant price leadership cartel. We consider stability concepts such as the farsighted core, the farsighted stable sets, and the largest consistent set. We show that: (i) the farsighted core is either an empty set or a singleton set of the grand cartel; (ii) any Pareto efficient cartel is itself a farsighted stable set; and (iii) the set of cartels in which fringe firms enjoy higher profits than the firms in the minimal Pareto efficient cartel is the largest consistent set.     

Core-stable rings in auctions with independent private values

We propose a semi-cooperative game theoretic approach to check whether a given coalition is stable in a Bayesian game with independent private values. The ex ante expected utilities of coalitions, at an incentive compatible (noncooperative) coalitional equilibrium, describe a (cooperative) partition form game. A coalition is core-stable if the core of a suitable characteristic function, derived from the partition form game, is not empty. As an application, we study collusion in auctions in which the bidders? final utility possibly depends on the winner?s identity. We show that such direct externalities offer a possible explanation for cartels? structures (not) observed in practice.     

von Neumann–Morgenstern stable sets of income tax rates in public good economies

This paper studies the von Neumann–Morgenstern stable sets in a public good economy, where any allocation is achieved through a proportional income tax system. The outcome of the economy is defined to be a set of tax rates. We show that whenever the core as the set of tax rates is nonempty, it is a unique stable set. When the core is empty, the set of tax rates is a stable set if and only if the set is a singleton consisting of a tax rate satisfying a certain condition. We show the existence of such stable sets. The author is grateful to Mikio Nakayama, Jun Wako and an anonymous referee for their helpful comments and suggestions. He is also grateful to Youngsub Chun, Takuya Masuzawa and Shigeo Muto for their helpful comments.     

NEOCLASSICAL GROWTH AND THE DISTRIBUTION OF CONSUMPTION

Abstract.  The neoclassical growth model is used to compare an economy with growing per capita income with an economy with stationary per capita income, in terms of equity in distribution of consumption. The economies have the same initial conditions including the same initial wealth distribution. The outcome of the comparison depends on the nature of structural differences between the economies. Even with convergence in wealth distribution in the growing economy, the consumption distribution there may be less equitable and dynasties with least initial levels of wealth may be worse off than dynasties with same initial wealth levels in the stationary economy.     

Efficiency and equilibrium when preferences are time-inconsistent

We consider an exchange economy with time-inconsistent consumers whose preferences are additively separable. If consumers have identical discount factors, then allocations that are Pareto efficient at the initial date are also renegotiation-proof. In an economy with a sequence of markets, competitive equilibria are Pareto efficient in this sense, and for generic endowments, only if preferences are locally homothetic.     

Edgeworth's conjecture with infinitely many commodities: commodity differentiation

Summary. Convergence of the cores of finite economies to the set of Walrasian allocations as the number of agents grows has long been taken as one of the basic tests of perfect competition. The present paper examines this test in the most natural model of commodity differentiation: the commodity space is the space of nonnegative measures, endowed with the topology of weak convergence. In Anderson and Zame [12], we gave counterexamples to core convergence in L ¹, a space in which core convergence holds for replica economies and core equivalence holds for continuum economies; in addition, we gave a core convergence theorem under the assumption that traders' utility functions exhibit uniformly vanishing marginal utility at infinity. In this paper, we provide two core convergence results for the commodity differentiation model. A key technical virtue of this space is that relatively large sets (in particular, closed norm-bounded sets) are compact. This permits us to invoke a version of the Shapley-Folkman Theorem for compact subsets of an infinite-dimensional space. We show that, for sufficiently large economies in which endowments come from a norm bounded set, preferences satisfy an equidesirability condition, and either (i) preferences exhibit uniformly bounded marginal rates of substitution or (ii) endowments come from an order-bounded set, core allocations can be approximately decentralized by prices. Received: July 29, 1996; revised version: January 14, 1997     

The stability of decision making in committees: The one-core

We study the stability of decision making in committees. A policy proposal introduced by a committee member is either adopted or abandoned in favor of a new proposal after deliberations. If a proposal is abandoned, it is in spite of the committee member who introduced it, who does not cooperate in any effort to defeat it. Shenoy (1980) proposes the one-core as a solution concept for this game, and shows that this solution may be empty. We provide a necessary and sufficient condition for the existence of a stable policy under the majority rule. This result highlights a trade-off between the size of a committee, the number of competing policy options, and the existence of a stable outcome. Our findings imply a tension between political stability and the existence of a large number of competing interests in democracies.     

Theorems on correspondences and stability of the core

In this note two theorems strengthening Grodal's (1971) Theorem on correspondences are proved. The first drops the convexity assumption. The second strengthens that theorem further for the case when the range is the positive orthant. In this case, the conclusion of Grodal's Theorem - the intersection of the integral with the interior of the range being open- is modified to read as the integral being a relative open subset of the positive orthant. An example is provided to show that, such a strengthening is not valid in general. This allows us to dispense with the requirment of convexity of preferences in Grodal's (1971) theorems on the closedness of the set of Pareto optimal allocations, the core, and the continuity of the core correspondence for pure exchange economies. We apply this result to show that blocking coalitions in a large economy are stable. Received: September 30, 1998; revised version: September 18, 2001 RID="*" ID="*" The author is grateful to an anonymous referee for helpful comments. The usual disclaimer applies.     

Economies with observable types

We study economies of asymmetric information with observable types. Trade takes place in lotteries. Individuals face a standard budget constraint, while the incentive compatibility constraints are imposed on the production set of the intermediaries. This formalization encompasses moral hazard, as in [Jerez, 2003] and [Jerez, 2005], and private information economies. Equilibrium allocations are constrained efficient, but, contrary to what stated for example in Jerez (2005), the set of equilibrium allocations may be empty and the Second Welfare Theorem may fail. This happens for two reasons. First, constrained efficient allocations may violate the necessary and sufficient conditions of price supportability for the individuals. Second, even when constrained efficient allocation are price supportable, they may fail to be a profit maximizing choice of the firm at the individual supporting prices. To restore existence of an equilibrium the firm has to be restricted to supply allocations with support in the set of incentive compatible contracts.     

Uncertainty and the specificity of human capital

This paper studies the choice between general and specific human capital. A trade-off arises because general human capital, while less productive, can easily be reallocated across firms. Accordingly, the fraction of individuals with specific human capital depends on the amount of uncertainty in the economy. Our model implies that while economies with more specific human capital tend to be more productive, they also tend to be more vulnerable to turbulence. As such, our theory sheds some light on the experience of Japan, where human capital is notoriously specific: while Japan benefited from this predominately specific labor force in tranquil times, this specificity may also have been at the heart of its prolonged stagnation.     

A pitchfork bifurcation in the tatonnement process★

Summary . This note extends the example of Gale (1963) by considering the continuous time tatonnement process for a class of two agent, two commodity exchange economies, parametrized by a number μ∈(0,1). We demonstrate that as the parameter passes a threshold value μ^* the unique, globally stable competitive equilibrium loses local stability while two new locally stable equilibria appear. Intuitively, as μ increases the income effect become increasingly more important relative to substitution effect, and eventually overwhelms the latter. As the parameter μ approaches 1, the economy tends to the example considered by Gale, as does the limiting behavior of the tatonnement. Received: February 28, 1996; revised version August 5, 1996     

Stability of jurisdiction structures under the equal share and median rules

We consider a finite society with of individuals distributed along the real line. The individuals form jurisdictions to consume public projects, equally share their costs and, in addition, bear a transportation cost to the location of the project. We examine a core and Nash notions of stable jurisdiction structures and show that in hedonic games both solution sets could be empty. We demonstrate that in a quasi-hedonic set-up there is a Nash stable partition, but, in general, there are no core stable partitions. We then examine a subclass of societies that admits the existence of both types of stable partitions. Financial support through grants R98-0631 from the Economic Education and Research Consortium, # NSh-1939.2003.6 School Support, Russian Foundation for Basic Research No. 04-02-17227, and the Russian Science Support Foundation is gratefully acknowledged.