Exchange economies with asymmetric information: competitive equilibrium and core

Summary. A replica theorem is shown to hold for exchange economies with asymmetric information. In a replicated exchange economy with asymmetric information the set of all core elements with equal treatment is nonempty, but it is in general only a subset of the core. Nevertheless, the replica theorem and the presence of at least one core element with equal treatment suffice to show existence of a competitive quasi-equilibrium. Conditions on the initial endowments and the communication system are given to ensure that every competitive quasi-equilibrium is a competitive equilibrium.Received: 24 February 2003, Revised: 3 July 2003JEL Classification Numbers: C70, D50, D82.I thank an anonymous referee whose comments led to an improvement of the paper.     

Equilibrium theory with asymmetric information and with infinitely many commodities

The traditional deterministic general equilibrium theory with infinitely many commodities cannot cover economies with private information constraints on the consumption sets. We bring the level of asymmetric information equilibrium theory at par with that of the deterministic one. In particular, we establish results on equilibrium existence for exchange economies with asymmetric (differential) information and with an infinite dimensional commodity space. Our new equilibrium existence theorems include, as a special case, classical results, e.g. Bewley [Existence of equilibria in economies with infinitely many commodities, J. Econ. Theory 4 (1972) 514-540] or Mas-Colell [The price equilibrium existence problem in topological vector lattices, Econometrica 54 (1986) 1039-1053].     

Convergence of the Aumann–Davis–Maschler and Geanakoplos bargaining sets

Summary. Geanakoplos [17] defined a notion of bargaining set, and proved that his bargaining set is approximately competitive in large finite transferable utility (TU) exchange economies with smooth preferences. Shapley and Shubik [26] showed that the Aumann–Davis–Maschler bargaining set is approximately competitive in replica sequences of TU exchange economies with smooth preferences. We extend Geanakoplos result to nontransferable utility (NTU) exchange economies without smooth preferences, and we extend the Shapley and Shubik result to non-replica sequences of NTU exchange economies with smooth preferences.Received: November 11, 1996This revised version was published online in February 2005 with corrections to the cover date.     

Perfect competition in asymmetric information economies: compatibility of efficiency and incentives

The idea of perfect competition for an economy with asymmetric information is formalized via an idiosyncratic signal process in which the private signals of almost every individual agent can influence only a negligible group of agents, and the individual agents’ relevant signals are essentially pairwise independent conditioned on the true states of nature. Thus, there is no incentive for an individual agent to manipulate her private information. The existence of incentive compatible, ex post Walrasian allocations is shown for such a perfectly competitive asymmetric information economy with or without “common values”. Consequently, the conflict between incentive compatibility and Pareto efficiency is resolved exactly, and its asymptotic version is derived for a sequence of large, but finite private information economies.     

The core of an exchange economy with asymmetric information

This paper studies the core of an exchange economy in which agents are asymmetrically informed about states of nature. An agent's information is modelled as part of his consumption set and thus as part of his consumption plans. If an agent joins a coalition, his information changes according to an exogenously given information rule, a concept introduced by B. Allen. It is shown that an exchange economy with asymmetric information generates a well defined cooperative game and that the core of this game and thus the core of the underlying economy is nonempty. In contrast to recent results, this holds independently of the given information rule.     

Information transmission in coalitional voting games

A core allocation of a complete information economy can be characterized as one that would not be unanimously rejected in favor of another feasible alternative by any coalition. We use this test of coalitional voting in an incomplete information environment to formalize a notion of resilience. Since information transmission is implicit in the Bayesian equilibria of such voting games, this approach makes it possible to derive core concepts in which the transmission of information among members of a coalition is endogenous. Our results lend support to the credible core of Dutta and Vohra [Incomplete information, credibility and the core, Math. Soc. Sci. 50 (2005) 148-165] and the core proposed by Myerson [Virtual utility and the core for games with incomplete information, Mimeo, University of Chicago, 2005] as two that can be justified in terms of coalitional voting.     

ECONOMIC NETWORKING AND STABILITY

Abstract. In this paper we discuss finite economies with the presence of transaction costs and with decreasing, constant or increasing returns. In general such an economy may have no general equilibrium existence and may even have an empty core. We analyse the trading networks of such an economy, introducing the concepts of locally stable network structure, un‐dominated locally stable network structures and most stable network structures. We point out that the set of most stable network structures could be treated as a solution concept for the empty core economies both in theoretical analysis and in application.     

On the uniqueness of fully informative rational expectations equilibria

Summary. This paper analyzes two equivalent equilibrium notions under asymmetric information: risk neutral rational expectations equilibria (rn-REE), and common knowledge equilibria. We show that the set of fully informative rn-REE is a singleton, and we provide necessary and sufficient conditions for the existence of partially informative rn-REE. In a companion paper (DeMarzo and Skiadas (1996)) we show that equilibrium prices for the larger class of quasi-complete economies can be characterized as rn-REE. Examples of quasi-complete economies include the type of economies for which demand aggregation in the sense of Gorman is possible (with or without asymmetric information), the setting of the Milgrom and Stokey no-trade theorem, an economy giving rise to the CAPM with asymmetric information but no normality assumptions, the simple exponential-normal model of Grossman (1976), and a case of no aggregate endowment risk. In the common-knowledge context, we provide necessary and sufficient conditions for a common knowledge posterior estimate, given common priors, to coincide with the full communication posterior estimate. Received: May 29, 1997; revised version: July 18, 1997     

A testable model of consumption with externalities

This paper presents a nonparametric model of interdependent preferences, where an individual's consumption may act as an externality on the preferences of other consumers. We assume that individual price consumption data is observed for all consumers. It is known that the general consumption model with externalities imposes few restrictions on the observed data, where the consistency requirement is Nash rationalizability. We motivate potential games as an important sub class of games where the family of concave potential games is refutable and imposes stronger restrictions on observed data. We use this framework to extend the analysis of Brown and Matzkin [D. Brown, R. Matzkin, Testable restrictions on the equilibrium manifold, Econometrica 64 (1996) 1249-1262] on refutable pure exchange economies to pure exchange economies with externalities. Finally, we discuss an application of this model to inter-household consumption data.     

Trade and revelation of information

We consider an economy with asymmetric information and two types of agents, fully informed and uninformed. Uninformed agents update their information observing equilibrium prices and the equilibrium levels of other agents’ excess demand. We show that, for a generic set of economies, there are rational expectations equilibria which are partially revealing on an open, dense set of signals of positive Lebesgue measure, provided that the dimension of the signal space is sufficiently larger than the dimension of the commodity space.     

On mixed markets with asymmetric information

In asymmetric information exchange economies involving both non-negligible and negligible agents, one should expect the failure of the private Core-Walras Equivalence Theorem. This paper shows that if “large” traders are similar to each other, then they lose their market power and hence the Equivalence Theorem can be restored. We also investigate on weaker equivalences among Walrasian expectations allocations, Aubin private core and private core allocations of the original mixed economy and the atomless one associated to it, without the assumption that all atoms are of the same type. Furthermore, extensions of Hervés-Moreno-Yannelis and Schmeidler Theorems (compare Hervés et al. in J Math Econ 41:844–856, 2005a; Schemidler in Econometrica 40:579–580, 1972) are given for differential information economies in which the feasibility constraints are imposed with an equality (exact feasibility).     

Interim efficiency with MEU-preferences

Recently Kajii and Ui (2009) [17] proposed to characterize interim efficient allocations in an exchange economy under asymmetric information when uncertainty is represented by multiple posteriors. When agents have Bewley's incomplete preferences, Kajii and Ui (2009) [17] proposed a necessary and sufficient condition on the set of posteriors. However, when agents have Gilboa-Schmeidler's MaxMin expected utility preferences, they only propose a sufficient condition. The objective of this paper is to complete Kajii and Ui's work by proposing a necessary and sufficient condition for interim efficiency for various models of ambiguity aversion and in particular MaxMin expected utility. Our proof is based on a direct application of some results proposed by Rigotti, Shannon and Stralecki (2008) [24].     

Dynamic coalitional equilibrium

We study coalition formation processes of Konishi and Ray (2003) [27]. It is shown that an absorbing and deterministic process of coalition formation that also forms an equilibrium - satisfies a coalitional one-deviation property - does exist if one allows the process to be history dependent. All such dynamic equilibrium processes of coalition formation are characterized. Absorbing outcomes of dynamic equilibrium processes are also identified. It is shown that they always constitute a subset of the largest consistent set of Chwe (1994) [11]. A procedure that identifies a dynamic equilibrium process of coalition formation in finite time is constructed.     

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.     

Competitive and core allocations in large economies with differential information

Summary. We study the core and competitive allocations in exchange economies with a continuum of traders and differential information. We show that if the economy is “irreducible”, then a competitive equilibrium, in the sense of Radner (1968, 1982), exists. Moreover, the set of competitive equilibrium allocations coincides with the “private core” (Yannelis, 1991). We also show that the “weak fine core” of an economy coincides with the set of competitive allocations of an associated symmetric information economy in which the traders information is the joint information of all the traders in the original economy. Received March 22, 2000; revised version: May 1, 2000     

Pairwise kidney exchange: Comment

In their recent paper, Roth et al. [Pairwise kidney exchange, J. Econ. Theory 125 (2005) 151-188] consider pairwise kidney exchanges, and show within this subset of feasible exchanges that a priority mechanism is strategy-proof. We show that this result can be broadened to allow much more general mechanisms and restrictions on the feasible set of allocations, including allowing three-way exchanges, regional specifications, and others. The key requirement is that the choice mechanism be consistent, i.e., if an allocation is chosen from some set of feasible allocations, it is also chosen from any subset of that set.     

International Tax Competition: There is No Need for Cooperation in Information Sharing

A model is investigated in which small open economies choose the degree of information exchange among tax authorities and an unrestricted set of capital income taxes. The author shows that cooperation in information sharing does not matter in equilibrium outcomes. This comes in striking contrast to existing results and the common belief among policy practitioners. The reason for this result is that if the set of distortionary taxes is unrestricted then, depending on the characteristics of the economy, either information sharing becomes redundant or the non‐cooperative equilibrium is characterized by zero information exchange and overprovision of information.     

Equivalence of Lindahl equilibrium with participation prices and the core

Summary In a model of an economy with multiple public goods and differentiated crowding, it is shown that asymptotically the core has the equal treatment property and coincides with the equilibrium outcomes. It follows that all individuals of the same type in the same jurisdiction must pay the same Lindahl taxes and, with strict convexity of preferences, the same Lindahl prices. With only one private good, for sufficiently large economies we show (a) the equivalence of the core and the set of equilibrium outcomes and (b) the nonemptiness of approximate cores and their equivalence to the set of approximate equilibrium outcomes.The author is indebted to Vicky Barham, John Conley, Hideo Konishi, Julian Manning and Roma Jakiwczyk for comments on an earlier draft of this paper. The author gratefully acknowledges the research support of the Social Sciences and Humanities Research Council of Canada.