The bargaining set of a large economy with differential information

Summary. We study the Mas-Colell bargaining set of an exchange economy with differential information and a continuum of traders. We established the equivalence of the private bargaining set and the set of Radner competitive equilibrium allocations. As for the weak fine bargaining set, we show that it contains the set of competitive equilibrium allocations of an associated symmetric information economy in which each trader has the “joint information” of all the traders in the original economy, but unlike the weak fine core and the set of fine value allocations, it may also contain allocations which are not competitive in the associated economy. Received: February 15, 1999; revised version: August 9, 1999     

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     

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.     

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     

Fair allocations in large economies

The purpose of this paper is the study of problems of equity in an economy with many agents. Conditions are given under which every equitable and Pareto optimal allocation is a competitive equilibrium with equal incomes for all agents. The results are also of potential relevance for the literature on incentive compatibility since the allocations that are obained through incentive mechanisms in large economies turn out to be equitable.     

Growth in economies with non convexities: sunspots and lottery equilibria

Summary. We investigate the relation between lotteries and sunspot allocations in a dynamic economy where the utility functions are not concave. In an intertemporal competitive economy, the household consumption set is identified with the set of lotteries, while in the intertemporal sunspot economy it is the set of measurable allocations in the given probability space of sunspots. Sunspot intertemporal equilibria whenever they exist are efficient, independently of the sunspot space specification. If feasibility is, at each point in time, a restriction over the average value of the lotteries, competitive equilibrium prices are linear in basic commodities and intertemporal sunspot and competitive equilibria are equivalent. Two models have this feature: Large economies and economies with semi-linear technologies. We provide examples showing that in general, intertemporal competitive equilibrium prices are non-linear in basic commodities and, hence, intertemporal sunspot equilibria do not exist. The competitive static equilibrium allocations are stationary, intertemporal equilibrium allocations, but the static sunspot equilibria need not to be stationary, intertemporal sunspot equilibria. We construct examples of non-convex economies with indeterminate and Pareto ranked static sunspot equilibrium allocations associated to distinct specifications of the sunspot probability space.Received: 25 August 2003, Revised: 16 March 2004, JEL Classification Numbers: D84, D90.Correspondence to: Paolo SiconolfiWe thank Herakles Polemarchakis for helpful conversations on the topic. The research of Aldo Rustichini was supported by the NSF grant NSF/SES-0136556.     

Peer group effects in applied general equilibrium

Summary. In this paper, I develop an applied general equilibrium environment with peer group effects. The application I consider is schooling. The framework used here is general equilibrium with clubs. I establish the existence of equilibrium for the economy with a finite number of school types. This result is then extended to the case where the set of school types is a continuum. The two welfare theorems are shown to hold for both economies. To compute the equilibrium, I construct a Negishi mapping from the set of weights on individual type's utility to the set of transfers that support the corresponding Pareto allocations as competitive equilibria with transfers. Because this mapping is a correspondence, a version of Scarf's algorithm is used to find a competitive equilibrium. Received: June 9, 1999; revised version: March 13, 2000     

A three way equivalence

In view of the well known core equivalence results in atomless economies, coincidence of market game equilibrium allocations with competitive allocations is tantamount to a three way equivalence between market game mechanisms, competitive equilibria and the core. Based on this idea we study equilibrium refinements of market games, which allow us to use the core equivalence machinery in order to provide an exact market game characterization of competitive equilibria.     

Correlated equilibrium and sunspot equilibrium

Summary We show by an example that the sunspot equilibria of a competitive economy are not equivalent to the correlated equilibria if sunspots generate transfers between (extrinsic) states of nature (through a contingent commodities market). Nevertheless, we prove that the sunspot equilibrium allocations of a standard overlapping generations economy coincide with the (strategic form) correlated equilibrium allocations of a natural market game mimicking the economy.     

Short run core equivalence in an overlapping generations model

This essay establishes the equality between the set of competitive equilibrium allocations and the set of allocations which belong to the cores of a sequence of short run economies for an overlapping generations model. A short run economy is a finite period economy obtained by truncating the original economy so that the truncated economy is irreducible.     

INCENTIVE EFFICIENT PRICE SYSTEMS IN LARGE INSURANCE ECONOMIES WITH ADVERSE SELECTION

We decentralize incentive efficient allocations in large adverse selection economies by introducing a competitive market for mechanisms, that is, for menus of contracts. Facing a budget constraint, informed individuals purchase (lottery) tickets to enter mechanisms, whereas firms sell tickets and supply slots at mechanisms at given prices. Beyond optimization, market clearing, and rational expectations, an equilibrium requires that firms cannot favorably change, or cut, prices. An equilibrium exists and is incentive efficient. An equilibrium can be computed as the solution to a programming problem that selects the incentive efficient outcome preferred by the highest type within an appropriately defined set. For two‐types economies, this is the only equilibrium outcome.     

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     

The efficiency of competitive mechanisms under private information

We consider the efficiency properties of exchange economies where privately informed traders behave strategically. Specifically, a competitive mechanism is any mapping of traders’ reports about their types to an equilibrium price vector and allocation of the reported economy. In our model, some traders may have non-vanishing impact on prices and allocations regardless of the size of the economy. Although truthful reporting by all traders cannot be achieved, we show that, given any desired level of approximation, there is such that any Bayesian-Nash equilibrium of any competitive mechanism of any private information economy with or more traders leads, with high probability, to prices and allocations that are close to a competitive equilibrium of the true economy. In particular, allocations are approximately efficient. A key assumption is that there is small probability that traders behave non-strategically.     

A Core‐Equilibrium Convergence in a Public Goods Economy

This paper shows a core‐equilibrium convergence in a public goods economy where consumers' preferences display warm glow effects. We demonstrate that if each consumer becomes satiated to other consumers' provision, then as the economy grows large the core shrinks to the set of Edgeworth allocations. Moreover, we show that an Edgeworth allocation can be decentralized as a warm glow equilibrium.     

Indeterminate Balanced Growth under Habit Persistence and Fiscal Policies

This paper studies a dynamic general equilibrium model with habit persistence in preferences and fiscal policies of taxation and expenditures. Preference takes a subtractive form of habits (the marginal rate of substitution between the agent's own consumption and habit stocks is constant), and technology is linear in aggregate capital (the economy grows without a limit in the long run). We find a continuum of competitive equilibrium paths in conjunction with a unique balanced growth path in the growing economy, in which habits represent both envy/jealousy and altruism/admiration. In addition, in the social optimum under second-best fiscal policies, we show the existence of indeterminacy in transitional allocations along with a unique balanced growth path. Thus, we find that the introduction of habits influences the patterns of the transitional paths but has no impact on the balanced growth path in either competitive or social optimum allocations. The second-best fiscal policy, therefore, restores the socially optimal balanced growth rate but fails to select the unique transitional path among multiple competitive equilibrium paths in the imperfectly competitive economy.     

Private Value Allocations in Large Economies with Differential Information

We consider a Radner-type (e.g., Radner, 1968, Econometrica36, 31–58) pure exchange economy with differential information and a continuum of agents. We show that under appropriate assumptions the set of Aumann–Shapley private value allocations in such an economy coincides with the set of Radner competitive equilibrium allocations. Journal of Economic Literature Classification Numbers: C71, D51, D82.     

Balance–of–Payments Equilibrium and the Determinacy of Interest Rates

In a world economy of overlapping generations with multiple countries, a competitive equilibrium need not satisfy the condition that the balance of payments be in equilibrium. The requirement that, in addition to market clearing, a balance–of–payments equilibrium condition be satisfied selects Pareto–optimal allocations and guarantees the determinacy of equilibrium.     

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.     

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     

Optimal growth with many consumers

A method is described for constructing all Pareto-optimal allocations for a dynamic economy with many heterogeneous consumers, under certainty, in which both the technology and consumer preferences are recursive but preferences need not be additively separable over time. Optimal (perfect foresight competitive equilibrium) allocations are obtained through the study of a dynamic program. For an economy with one consumption good, sufficient conditions are given for the existence of a unique interior stationary distribution of consumption and wealth. For a two-person exchange economy, sufficient conditions are given for the global asymptotic stability of the unique interior stationary point.