On the core and Walrasian expectations equilibrium in infinite dimensional commodity spaces

In this paper, we establish two different characterizations of Walrasian expectations allocations by the veto power of the grand coalition in an asymmetric information economy having finitely many agents and states of nature and whose commodity space is a Banach lattice. The first one deals with Aubin non-dominated allocations, and the other claims that an allocation is a Walrasian expectations allocation if and only if it is not privately dominated by the grand coalition, by considering perturbations of the original initial endowments in precise directions.     

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.     

Walrasian versus quasi-competitive equilibrium and the core of a production economy

Summary. This paper presents very general conditions guaranteeing that a quasi-competitive equilibrium is a Walrasian equilibrium. We also develop a generalization (and a simplified proof) of Nikaidos and McKenzies extensions of the classic Debreu-Scarf theorem on core convergence, and apply the first result to obtain an equivalence between the set of Edgeworth equilibria and the set of Walrasian equilibria in a production economy.Received: 6 September 2002, Revised: 14 November 2003, JEL Classification Numbers: C71, D50, D51.     

Union games: technological unemployment

Summary. Given a production economy, we define union games by considering strategic behavior of the suppliers of factors. We refer to the Nash equilibria of this game as union equilibria. We analyze situations where the unemployment of factors is supported as a union equilibrium. The degree of unemployment depends on technological conditions. This allows us to model a source of unemployment which differs from the usual sources provided in the literature. We state a limit result that demonstrates that, as the market power of unions decreases, the corresponding sequence of union equilibria converges to the Walrasian equilibrium, that is, to full employment of factors. We also provide some examples that illustrate the main results.Received: 21 October 2004, Revised: 14 December 2004, JEL Classification Numbers: D51, C72. Correspondence to: Emma Moreno-GarcíaE. Moreno acknowledges financial support from the Research Grant BEC2000-1388-C04-01 (Ministerio de Ciencia y Tecnología and FEDER). G. Fernández de Córdoba and E. Moreno acknowledge financial support from the Research Grant SA091/02 from Junta de Castilla y León. We are indebted to C. Alós-Ferrer, C. Pita, D. Anisi, J. A. Ortega, F. Jimeno, J. P. Torres-Martínez, M. Steinert and C. Hervés for helpful comments and insights. We are particularly grateful to T. Kehoe and an anonymous referee for suggestions that improved this paper.     

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.     

The equilibrium of the bargaining game and core convergence theorem on an exchange economy with limited traders

Debreu and Scarf (1963), Hildenbrand (1974), Aumann (1964), Dierker (1975), Bewley (1973), and others have shown that the core of an exchange economy with infinitely many or finitely many traders converges. However, an exchange economy does not always consist of infinitely many or finitely many traders. This note provides proof of the core convergence theorem on an exchange economy with limited traders by a bargaining game methodology. The main contribution of this note is to innovate the equilibrium solution to the bargaining game in the exchange economy. In this note, the concept of common payoff is introduced; in the bargaining game of a coalition on its common payoff, all coalition members will get the same distribution, thus the distribution scheme of the cooperation surplus of the exchange economy is determined. This note shows that the bargaining game among the traders on the distribution of the cooperation surplus will make the pure exchange economy with limited traders converge to the Walrasian equilibrium, all the allocations other than the Walrasian equilibrium will be eliminated from the core of this economy.     

Decentralizing lottery allocations in markets with indivisible commodities

Summary In economies with indivisible commodities, consumers tend to prefer lotteries in commodities. A potential mechanism for satisying these preferences is unrestricted purchasing and selling of lotteries in decentralized markets, as suggested in Prescott and Townsend [Int. Econ. Rev.25, 1–20]. However, this paper shows in several examples that such lottery equilibria do not always exist for economies with finitely many consumers. Other conditions are needed. In the examples, equilibrium and the associated welfare gains are realized if consumptions are bounded or if lotteries are based upon a common sunspot device as defined by Shell [mimeo, 1977] and Cass and Shell [J. Pol. Econ.91, 193–227]. The paper shows that any lottery equilibrium is either a Walrasian equilibrium or a sunspot equilibrium, but there are Walrasian and sunspot equilibria that are not lottery equilibria.This paper is based on Chapter 3 of my doctoral dissertation, written while I was a student at Cornell University. I thank Larry Blume, Yue Yun Chen, David Easley, Aditya Goenka, John Marshall, Bruce Smith, John Wooders and an anonymous referee. I am particularly grateful to Karl Shell and Cheng-Zhong Qin. I thank the Academic Senate at UCSB for financial support.     

Microeconomic uncertainty and macroeconomic indeterminacy

We propose a stylized intertemporal macroeconomic model wherein the combination of decentralized trading and microeconomic uncertainty (taking the form of privately observed and uninsured idiosyncratic shocks) creates an information problem between agents and generates indeterminacy of the macroeconomic equilibrium. For a given value of the economic fundamentals, the economy admits a continuum of equilibria that can be indexed by the sales expectations of firms at the time of investment. The Walrasian equilibrium is one of these possible equilibria but it is reached only if firms are optimistic enough. With a weaker degree of optimism, equilibrium output, employment and real wages will be lower than in the Walrasian equilibrium. Moreover, the range of possible equilibria will depend positively on the wage elasticity of the labour supply and on the magnitude of the information problem between buyers and sellers (in our case, the variance of the idiosyncratic shocks).Stochastic simulations performed on a calibrated version of the model show that pure demand expectation shocks may generate business cycle statistics that are not inconsistent with the observed ones.     

On Nash implementation of Walrasian equilibria in a market for pure indivisibles without money

This paper deals with the Walrasian property of Nash and strong equilibria of a specific strategic market game which refers to a pure exchange economy involving purely indivisible commodities and no money. The game is of sealed-bid auction type and it is shown that any Nash equilibrium at which no agent is in status quo is a strong equilibrium and implements a Walrasian equilibrium. Moreover, it appears that two modifications of the game's rules ensure that any strong equilibrium outcome is Walrasian. These results are identical to those obtained by Svensson for markets involving purely indivisible goods and money.     

The core of an economy with satiation

Summary. It has long been known that in economies with satiation, the set of competitive equilibria does not coincide with the limiting core of an economy. In dividend equilibria, introduced independently by a number of authors, the budget excess is allowed to be divided among consumers as dividends and equilibrium existence is restored. In this paper a new notion of blocking which leads to core - dividend equilibrium equivalence is introduced. Specifically, it is shown that an allocation is a dividend equilibrium if and only if a corresponding equal treatment allocation of a large economy is in the core.Received: 21 June 2003, Revised: 3 December 2003, JEL Classification Numbers: D50.Alexander Konovalov: The author would like to thank M. Florig, P. J. J. Herings, V. Marakulin, D. Talman, V. Vasilev, and anonymous referees for helpful comments and suggestions.     

Sunspots,indeterminacy and Pareto inefficiency in economies with incomplete markets

Summary. We consider two periods economies with both intrinsic and extrinsic uncertainty. Asset markets are incomplete in the certainty economy. If assets are nominal, there are enough commodities and the number of agents is greater than two and smaller than the total number of states of nature tomorrow (minus one), then a sunspot-invariant equilibrium is generically Pareto dominated by some sunspot equilibria. When assets are real, and there are enough commodities, if there are sunspot equilibria, there are sunspot equilibria Pareto dominating sunspot-invariant equilibria under the same restriction on the number of agents (and stronger restrictions on the number of commodities).Received: 20 October 2003, Revised: 1 April 2004, JEL Classification Numbers: D52.I wish to thank Paolo Siconolfi for helpful suggestions and comments. I aknowledge the financial support of M.I.U.R. and the kind hospitality of C.C.D.R. in Summer 2003.     

Rational expectations in the overlapping generations model

This paper reports results on the character of the rational expectations equilibria of a stochastic overlapping generations model with heterogenous markets. The model considered is a stationary overlapping generations model in which the endowments of young agents are subject to i.i.d. random shocks. The main result shown is that if there are l > 1 commodities traded in every period, then for most preferences, the rational expectations equilibrium stochastic process of prices and allocations necessarily exhibits serial correlation. This is in marked contrast to the one commodity model in which there always exists an equilibrium which is measure isomorphic to the endowment process.     

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].     

Auctions of Heterogeneous Objects

Simultaneous sealed bid auctions of heterogeneous objects are analyzed. Each bidder's reservation value for an object depends upon the other objects he obtains. Bidders' reservation values are common knowledge. In simultaneous first-price auctions, the set of Walrasian equilibrium allocations contains the set of pure strategy Nash equilibrium allocations which in turn contains the set of strict Walrasian equilibrium allocations. Hence, pure strategy Nash equilibria (when they exist) are efficient. Mixed strategy Nash equilibria may be inefficient. In simultaneous second-price auctions, any efficient allocation can be implemented as a pure strategy Nash equilibrium outcome if a Walrasian equilibrium exists.Journal of Economic LiteratureClassification Numbers: D44, D51.     

Market clearing and derivative pricing

Summary. We develop a method of assigning unique prices to derivative securities, including options, in the continuous-time finance model developed in Raimondo (2001). In contrast with the martingale method of valuing options, which cannot distinguish among infinitely many possible option pricing processes for a given underlying securities price process when markets are dynamically incomplete, our option prices are uniquely determined in equilibrium in closed form as a function of the underlying economic data.Received: 14 April 2003, Revised: 7 January 2004, JEL Classification Numbers: G13, D52.This paper is dedicated to Birgit Grodal, whose strength and character we greatly admire. We are very grateful to Darrell Duffie, Steve Evans, Botond Koszegi, Roger Purves, Jacob Sagi, Chris Shannon, Bill Zame and an anonymous refereee for very helpful discussions and comments. The work of both authors was supported by Grant SES-9710424, and Andersons work was supported by Grant SES-0214164, from the National Science Foundation.     

Existence and optimality of oligopoly equilibria in linear exchange economies

Summary. We consider a linear exchange economy and its successive replicas. We study the notion of Cournot-Walras equilibrium in which the consumers use the quantities of commodities put on the market as strategic variables. We prove that, generically, if the number of replications is large enough but finite, the competitive behaviour is an oligopoly equilibrium. Then, under a mild condition, which may be interpreted in terms of market regulation and/or market activity, we show that any sequence of oligopoly equilibria of successive replica economies converges to the Walrasian outcome and furthermore that every oligopoly equilibrium of large, but finite, replica is Pareto optimal. Consequently, under the same assumptions on the fundamentals of the economy, one has an asymptotic result on the convergence of oligopoly equilibria to the Walras equilibrium together with a generic existence result for the Cournot-Walras. Received: June 20, 2002; revised version: November 20, 2002 RID="*" ID="*" Part of this paper was written while the second author was visiting the Universidad de Vigo. The support of the department of mathematics is gratefully acknowledged. Correspondence to: J.M. Bonnisseau     

Coalition Formation with Binding Agreements

We study coalition formation in "real time", a situation in which coalition formation is intertwined with the ongoing receipt of pay-offs. Agreements are assumed to be permanently binding: They can only be altered with the full consent of existing signatories. For characteristic function games we prove that equilibrium processes—whether or not these are history dependent—must converge to efficient absorbing states. For three-player games with externalities each player has enough veto power that a general efficiency result can be established. However, there exist four-player games in which all Markov equilibria are inefficient from every initial condition, despite the ability to write permanently binding agreements.     

Quasi-equilibria in Banach spaces with lower semi-continuous preferences

Summary. This paper establishes a general result on the existence of non-trivial quasi-equilibria for economies with infinitely many commodities, in which consumers preferences are assumed to be lower semi-continuous, but not necessarily to have open lower sections nor to be open valued. Such preference relations include the lexicographic orderings. In addition, production technologies are not required to satisfy free disposal condition.Received: 25 May 2004, Revised: Received: 25 May 2004; revised version: September: 14, 2004, JEL Classification Numbers: D51, D61, D62.I am grateful to Professors Sho-Ichiro Kusumoto, Atsushi Kajii, Yoshihiko Otani, Zaifu Yang and one anonymous referee for their helpful commente and suggestions.     

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.     

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