An extensive form interpretation of the private core

Summary. The private core of an economy with differential information, (Yannelis (1991)), is the set of all state-wise feasible and private information measurable allocations which cannot be dominated, in terms of ex ante expected utility functions, by state-wise feasible and private information measurable net trades of any coalition. It is coalitionally Bayesian incentive compatible and also takes into account the information superiority of an individual. We provide a noncooperative extensive form interpretation of the private core for three person games. We construct game trees which indicate the sequence of decisions and the information sets, and explain the rules for calculating ex ante expected payoffs. In the spirit of the Nash programme, the private core is thus shown to be supported by the perfect Bayesian equilibrium of a noncooperative game. The discussion contributes not only to the development of ideas but also to the understanding of the dynamics of how coalitionally incentive compatible contracts can be realized. Received: July 21, 2000; revised version: January 16, 2001     

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.     

Non-implementation of rational expectations as a perfect Bayesian equilibrium

Summary. We point out several conceptual difficulties of the rational expectations equilibrium concept. In particular we show that such an equilibrium need not be incentive compatible and need not be implementable as a perfect Bayesian equilibrium . A comparison of rational expectations equilibria with the private core is also provided. We conclude that the private core is a more appropriate concept to capture the idea of contracts under asymmetric information.Received: 15 December 2003, Revised: 18 November 2004, JEL Classification Numbers: C71, C72, D5, D82. Correspondence to: Nicholas C. YannelisWe wish to thank Dr A. Hadjiprocopis for his invaluable help with the implementation of Latex in a Unix environment.     

Stability and Largeness of the Core

In general, there are examples of TU games where the core is stable but is not large. In this paper, we show that the extendability condition introduced by Kikuta and Shapley (1986, “Core Stability in n-Person Games,” Mimeo) is sufficient for the core to be stable as well as large, for TU games with five or fewer players. We provide a counter example when the number of players is six. We then introduce a stronger extendability condition and show that it is necessary and sufficient for the core to be large. Our proof makes use of a well-known result from the theory of convex sets. Journal of Economic Literature Classification Number: C71.     

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     

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     

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.     

民营企业连锁经营中的核心能力共享

连锁经营运用现代化大工业生产原理、以获得规模效益为目的,这一经营形式近几年来被中国大多数企业运用,并取得了快速的发展。核心能力共享使连锁经营具有强大吸引力和很高的成功率,连锁经营的崛起也进一步促成了核心能力共享。应根据民营企业不同规模大小和核心能力状况,确定利用连锁进行扩张的不同形式,制定出连锁经营方式选择模型;并基于民营企业的核心能力共享,选择连锁经营的运作模式。     

Existence of Edgeworth equilibria for economies with asymmetric information

We analyze a general equilibrium model with asymmetrically informed agents. A basic and well-known consequence of asymmetric information is the failure of equal treatment property. Despite of this, we show that in every replica economy a private core allocation, which treats agents of the same type equally, exists. This result is provided in the framework of two different models, with and without expectations, and it suffices to guarantee in both cases the existence of a private Edgeworth equilibrium. The author is grateful to an anonymous referee for his/her careful reading and helpful comments and acknowledges support by Research Grant no. 2006132713-005 (Ministero Italiano dell’Università e della Ricerca).     

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     

How Should the Graduate Economics Core be Changed?

The authors present suggestions by graduate students from a range of economics departments for improving the first-year core sequence in economics. The students identified a number of elements that should be added to the core: more training in building microeconomic models, a discussion of the methodological foundations of model-building, more emphasis on institutions to motivate and contextualize macroeconomic models, and greater focus on econometric practice rather than theory. The authors hope that these suggestions will encourage departments to take a fresh look at the content of the first-year core.     

Private Information: Similarity as Compatibility

We introduce a new topology on information which evaluates the similarity between information fields taking into account their compatibility, that is, the events that are commonly observed. With this “topology of common information”, the Walrasian expectations equilibrium (Radner 1968) and the private core (Yannelis 1991) are upper semicontinuous     

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).     

Congestion effects in a public-good economy

This paper considers a public-good economy with congestion, where participants jointly produce a public good from input of a private good. This economic model gives rise to a transferable-utility game, the profit game, that depends on consumer preferences and a congestion parameter. The simplicity of the game allows the maximum level of congestion that guarantees the nonemptiness of the core of the economy to be determined. It is known that the sustainability of the Lindahl equilibrium in the core of the economy depends on the distribution of profits. In this paper two distributions of profits are compared: the Lindahl solution and the marginal-contribution solution. The latter is more often in the core than the Lindahl solution which in turn Lorenz-dominates the marginal-contribution solution.     

Equilibria in infinite-dimensional production economies with convexified coalitions

Summary. This paper deals with a private ownership production economy assuming that the commodity space is infinite-dimensional. It is first showed that the fuzzy core allocations, a concept that goes back to J.-P. Aubin, are in a one-to-one correspondence with certain core allocations of a continuum economy suitably defined. This result is obtained under convexity of preferences and production sets and separability of the commodity space. In the case of nonconvex preferences and production sets, the set of fuzzy coalitions can be enlarged in order to obtain that every allocation of the core accordingly defined is supported by a non zero price. The proof of the equivalence result when the positive cone of the commodity space has the empty interior, is obtained under assumptions of properness for preferences relations and production sets. Received: July 9, 1998; revised version: December 6, 1999     

Stable governments and the semistrict core

We consider the class of proper monotonic simple games and study coalition formation when an exogenous weight vector and a solution concept are combined to guide the distribution of power within winning coalitions. These distributions induce players' preferences over coalitions in a hedonic game. We formalize the notion of semistrict core stability, which is stronger than the standard core concept but weaker than the strict core notion and derive two characterization results for the semistrict core, depending on conditions we impose on the solution concept. A bounded power condition, which connects exogenous weights and the solution, turns out to be crucial. It generalizes a condition termed “absence of the paradox of smaller coalitions” that was previously used to derive core existence results.     

国有股权重、政策性负担与绩效——国有银行战略引资方案探析

本文结合当前国有银行战略引资的改革背景,构建银行业混合寡占、国有银行混合持股的古诺竞争均衡模型,研究认为战略引资后的均衡股权结构与国有银行所承担的政策性负担及私有银行数量密切相关;国有银行政策性负担与私有银行的经营绩效正相关,但从整体来看则损害了社会总福利.另外,政策性负担不影响市场可容纳的最大银行数量,但会影响达到这一数量时国有银行的股权结构.     

国有股权重、政策性负担与绩效——国有银行战略引资方案探析

We present a mixed oligopoly model for private banks and a public bank with mixed ownership and policy burden to research the program of strategic investor importing for state-owned banks. We find that close relationships exist among the equilibrium equity structure following strategic investor importing, the policy burden of state-owned banks and the number of private banks; that the policy burden of state-owned banks has positive relationships with the performance of private banks, with overall negative effect on social welfare; that the policy burden would not affect the maximum market capacity number of private banks but would affect the equity structure of state-owned banks with such a number.     

Is the Euro-Area core price index really more persistent than the food and energy price indexes?

The purpose of this paper is to measure the degree of persistence of the overall, core, food and energy Harmonized Indexes of Consumer Prices for the European Monetary Zone (HICP-EAs) and to identify its implications for decision-making in the private sector and in public policy.Using a non-parametric approach, our results demonstrate the presence of a statistically significant level of persistence in four HICP-EAs: headline, core, food and energy. Moreover, contrary to popular belief, the core index does not reflect permanent price changes. We also find evidence that the food and energy price indexes are more volatile and more persistent than the other two price indexes. Our results also show a reduction in persistence for both the headline and the core price indexes after the implementation of the single monetary policy, but not for food and energy.These results have important implications for both the private sector and for policymakers who use the core price index as a reference in their decision-making. In particular, core price index can lead to erroneous perception of price movements.     

Incentive compatibility and information superiority of the core of an economy with differential information

Summary We analyse the coarse, the fine, and the private core allocation of an exchange economy with differential information. The basic questions that we address are whether the above concepts are: (i) coalitionally incentive compatible, i.e., does truthful revelation of information in each coalition occur; and (ii) taking into account the information superiority or information advantage of an agent. Moreover, the above three concepts are examined in the presence of externalities and a comparison and interpretation of all of these core notions is provided.We wish to thank Stefan Krasa, Frank Page, Wayne Shafer, Anne Villamil, and Myrna Wooders for several useful comments, discussions, and suggestions. The comments of two referees were also helpful and we thank them for their careful reading. Obviously, we are responsible for any remaining errors.