Coalitional Bayesian Nash implementation in differential information economies

Summary. A mechanism coalitionally implements a social choice set if any outcome of the social choice set can be achieved as a coalitional Bayesian Nash equilibrium of a mechanism and vice versa. We say that a social choice set is coalitionally implementable if there is a mechanism which coalitionally implements it. Our main theorem proves that a social choice set is coalitionally implementable if and only if it is interim individually rational, interim efficient, coalitional B ayesian incentive compatible, and satisfies a coalitional Bayesian monotonicity condition as well as a closure condition. As an application of our main result, we show that the private core and the private Shapley value of an economy with differential information are coalitionally implementable. Received: January 12, 1998; revised version: March 30, 2000     

Coalitional strategy-proofness and fairness

This paper considers the problem of assigning a finite number of indivisible objects, like jobs, houses, positions, etc., to the same number of individuals. There is also a divisible good (money) and the individuals consume money and one object each. The class of fair allocation rules that are strategy-proof in the strong sense that no coalition of individuals can improve the allocation for all of its members, by misrepresenting their preferences, is characterized. It turns out that given a regularity condition, the outcome of a fair and coalitionally strategy-proof allocation rule must maximize the use of money subject to upper quantity bounds determined by the allocation rule. If available money is nonnegative, objects may be jobs and the distribution of money a wage structure. If available money is negative, the formal model may reflect a multi-object auction. In both cases fairness means equilibrium, i.e., that each individual receives a most demanded object. I would like to thank Tommy Andersson, Bo Larsson, Zaifu Yang and the participants of the seminars in Copenhagen and Lund for helpful comments on this paper. I will also thank an anonymous referee for very valuable comments. Financial support from The Jan Wallander and Tom Hedelius Foundation is gratefully acknowledged.     

Efficiency and incentive compatibility in differential information economies

Summary. We introduce several efficiency notions depending on what kind of expected utility is used (ex ante, interim, ex post) and on how agents share their private information, i.e., whether they redistribute their initial endowments based on their own private information, or common knowledge information, or pooled information. Moreover, we introduce several Bayesian incentive compatibility notions and identify several efficiency concepts which maintain (coalitional) Bayesian incentive compatibility. Received: March 25, 1996; revised September 5, 1996     

Non-myopic learning in differential information economies: the core

Summary. We study the process of learning in a differential information economy, with a continuum of states of nature that follow a Markov process. The economy extends over an infinite number of periods and we assume that the agents behave non-myopically, i.e., they discount the future. We adopt a new equilibrium concept, the non-myopic core. A realized agreement in each period generates information that changes the underlying structure in the economy. The results we obtain serve as an extension to the results in Koutsougeras and Yannelis (1999) in a setting where agents behave non-myopically. In particular, we examine the following two questions: 1) If we have a sequence of allocations that are in an approximate non-myopic core (we allow for bounded rationality), is it possible to find a subsequence that converges to a non-myopic core allocation in a limit full information economy? 2) Given a non-myopic core allocation in a limit full information economy can we find a sequence of approximate non-myopic core allocations that converges to that allocation? Received: May 25, 1999; revised version: August 9, 1999     

The measure of blocking coalitions in differential information economies

We provide an evaluation of the measure of privately blocking coalitions in differential information economies. In the case of atomless economies, it is proved that for a Pareto optimal allocation that is not a Walrasian expectations equilibrium, to any symmetric profile there corresponds a ball such that "almost half” of the profiles it contains are privately blocking. Analogous results are proved in the case of finite differential information economies for generalized coalitions and social coalition structures. From a different point of view, the paper can be considered as a contribution showing private core equivalence theorems under restrictions on coalition formation. We thank an anonymous referee for observations and comments improving an earlier version of the present paper.     

A market game approach to differential information economies

In this paper we recast a differential information economy as a strategic game in which players propose net trades and prices. Pure strategy Nash equilibria are strong and determine both consumption plans and commodity prices that coincide with the Walrasian Expectations equilibria of the underlying economy. The authors acknowledge support by research grants BEC2003-09067-C04-01 (Ministerio de Educación y Ciencia and FEDER), PGIDT04XIC30001PN (Xunta de Galicia) and SA070A05 (Junta de Castilla y León). JP Torres-Martínez is also grateful to CNPq-Brazil and University of Vigo for financial support. We are indebted to N.C. Yannelis for helpful comments and insights.     

On extensive form implementation of contracts in differential information economies

Summary. In the context of differential information economies, with and without free disposal, we consider the concepts of Radner equilibrium, rational expectations equilibrium, private core, weak fine core and weak fine value. We look into the possible implementation of these concepts as perfect Bayesian or sequential equilibria of noncooperative dynamic formulations. We construct relevant game trees which indicate the sequence of decisions and the information sets, and explain the rules for calculating ex ante expected payoffs. The possibility of implementing an allocation is related to whether or not it is incentive compatible. Implementation through an exogenous third party or an endogenous intermediary is also considered. Received: November 19, 2001; revised version: April 17, 2002 RID="*" ID="*" This paper comes out of a visit by Nicholas Yannelis to City University, London, in December 2000. We are grateful to Dr A. Hadjiprocopis for his invaluable help with the implementation of Latex in a Unix environment. We also thank Leon Koutsougeras and a referee for several, helpful comments. Correspondence to: N.C. Yannelis     

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     

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     

Large economies with differential information and without free disposal

We consider exchange economies with a continuum of agents and differential information about finitely many states of nature. It was proved in Einy et al. (Econ Theory 18, 321–332, 2001) that if we allow for free disposal in the market clearing (feasibility) constraints then an irreducible economy has a competitive (or Walrasian expectations) equilibrium, and moreover, the set of competitive equilibrium allocations coincides with the private core. However when feasibility is defined with free disposal, competitive equilibrium allocations may not be incentive compatible and contracts may not be enforceable (see e.g. Glycopantis et al. in Econ Theory 21, 495–526, 2002). This is the main motivation for considering equilibrium solutions with exact feasibility. We first prove that the results in Einy et al. (Econ Theory 18, 321–332, 2001) are still valid without free-disposal. Then, motivated by the issue of contracts’ execution, we adapt the incentive compatibility property introduced in Krasa and Yannelis (Econometrica 62, 881–900, 1994) and we prove that every Pareto optimal exact feasible allocation is incentive compatible, implying that contracts of competitive or core allocations are enforceable. We would like to thank two anonymous reviewers and the Associate Editor for their valuable suggestions and remarks. This work was partially done while V.F. Martins-da-Rocha was visiting the Dipartimento di Matematica e Informatica of the Università degli Studi di Perugia. We thank the audience of the First General Equilibrium Workshop at Rio. Section 6 dealing with contract enforcement and coalitional incentive compatibility has benefited from discussions with J. Correia-da-Silva, W. Daher, F. Forges, C. Hervès-Beloso, E. Moreno-García, K. Podczeck, Y. Vailakis and N.C. Yannelis.     

On the continuity of equilibrium and core correspondences in economies with differential information

Summary. We study upper semi-continuity of the private and coarse core and the Walrasian expectations equilibrium correspondences for economies with differential information, with Boylan (1971) topology on agents information fields.Received: 16 January 2004, Revised: 28 October 2004, JEL Classification Numbers: D50, D82, C70. Correspondence to: Ezra EinyWe wish to thank Carlos Herves, Nicholas Yannelis, and an anonymous referee for their helpful comments.     

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     

Private information in large economies

This paper examines the effect of private information in large economies. We show that in a model with stochastic information structures, the restrictions imposed on allocations by the presence of private information disappear in large economies. We also show that for a large class of direct mechanisms, the incentive for any agent to falsely report private information goes to zero as the number of agents becomes large. These results provide an “informational smallness” analog to existing “quantity smallness” limiting results in the literature.     

Sunk costs and fairness in incomplete information bargaining

We study a bilateral trading relationship in which one agent, the seller, can make a nonrecoverable investment in order to generate potential gains from trade. Afterwards, the seller makes a price offer that the buyer can either accept or reject. If agents are fairminded, sellers who are known by the buyer to have high investment costs are predicted to charge higher prices. If the investment cost is private information, low-cost sellers should price more aggressively and high-cost sellers less aggressively than under complete information, giving rise to disagreement and/or underinvestment. Our experiment support these predictions.     

Private information for foreign investment in emerging economies

In previous studies it has been found that new foreign investment is significantly related to the stock of existing investment in the country/region. This paper's contribution is the finding that a Japanese firm's new investment in an emerging economy is positively correlated with its own previous investment in that economy and also with the current/planned investments by competitors. These two channels are primarily substitutes; that is, investment by competitors becomes less salient when the firm has experience in the market. The correlated behaviour is not explained by industrial agglomerations but appears to reflect the value of private information to investment in emerging economies.
Information privée et investissement étranger dans les économies en émergence. Des travaux antérieurs ont montré que les nouveaux investissements à l'étranger sont co-reliés de manière significative à la taille du stock d'investissement étranger dans le pays ou la région. La contribution de ce mémoire porte sur le fait qu'un nouvel investissement d'une entreprise japonaise dans une économie en émergence est co-relié positivement avec son propre niveau antérieur d'investissement dans cette économie mais aussi avec le niveau des investissements présents et anticipés de ses concurrents. Ces deux canaux d'information sont des substituts: le niveau d'investissement par les concurrents devient moins important à proportion que l'entreprise a acquis de l'expérience dans ce marché. Ce comportement co-relié n'est pas expliqué par les effets d'agglomération industrielle mais semble refléter la valeur de l'information privée quand on investit dans des économies en émergence.     

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     

Balancedness and the core in economies with asymmetric information

Summary. A condition is given that is equivalent to balancedness of all NTU-games derived from an exchange economy with asymmetric information when endowments are variable. The condition is applicable to the ex-ante model with expected utilities, but also to the more general model of Arrow-Radner type economies without subjective probabilities. Differences in the interpretation of measurability assumptions between these two models are discussed, and another model with information consistent utility functions is developed in which the result would also hold. Received: December 12, 2001; revised version: November 1, 2002 RID="*" ID="*"I thank two anonymous referees whose comments led to an improvement of the paper.     

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.