Continuum Of Agents Research Articles

Trade using assets divisible at a cost

The consequences of costly divisibility of assets are studied using a model with the following features. The demand for assets is generated from an overlapping generations model with a continuum of agents in each generation and with intrageneration trade (intermediation) ruled out. There is a once-for-all supply of a stock of nonnegative-dividend assets in a large size, and there is a costly technology for dividing them into smaller sizes. Stationary equilibria are shown to exist. In contrast with similar models with costless divisibility of assets, competitive equilibria are not necessarily desirable; there can be Pareto-ordered equilibria.

On the Efficiency and Optimality of Allocations. II

In this work we study the problem of characterizing efficient, price efficient and optimal allocations in a very general economic model with a continuum of agents and an infinite-dimensional commodity space. We do that using the theory of concave normal integrands and Clarke’s theory of generalized gradients, as well as certain results from geometric functional analysis. We also consider approximations of those notions and study their properties using the theory of $\varepsilon $-subdiflerentiation and Ekeland’s variational principal. Then we examine those concepts in the context of a particular sector of the enonomy using single valued and multivalued conditional expectations and martingale theory. Finally we study stability questions using the Kuratowski–Mosco convergence of sets and the epi-convergence ($\tau $-convergence) of closed functions.

An expository note on individual risk without aggregate uncertainty

In economies where agents bear some risk, the analysis would often be facilitated by the assumption that the risks are i.i.d. and disappear in the aggregate. A formal appeal to the law of large numbers requires the consideration of a sequence of finite economies. In an economy with a continuum of agents there are countable families of sets for which it is impossible for a law of large numbers to be valid. With countably many agents and a finitely additive measure, independence is compatible with the law of large numbers.

Perfect competition in strategic market games with interlinked preferences

When the competitive system is viewed as a strategic market game with a continuum of agents, concern for others need not influence outcomes. The generalization of preference conditions is noted and discussed.

On a theorem of Schmeidler

Over a decade ago D. Schmeidler (1973) introduced a concept of non-cooperative equilibrium for games with a continuum of agents and, under a restriction on the payoff functions, established the existence of an equilibrium in pure strategies. The purpose of this note is to reformalize the model and the equilibrium notion of Schmeidler in terms of distributions rather than measurable functions. We shall see how once the definitions are available we get (pure strategy) equilibrium existence theorems quite effortlessly and under general conditions. A number of remarks contain applications to, among others, incomplete information games.

Equilibrium in abstract economies without ordered preferences and with a measure space of agents

We report a generalization of Aumann's (1966) existence theorem to economies without ordered preferences and with externalities in consumption. Our work can alternatively be viewed as a generalization of the Shafer–Sonnenschein (1975) theorem to economies with a continuum of agents.

Benzodiazepine receptor ligands with positive and negative efficacy

Recent studies have shown that benzodiazepine receptors can be affected not only by benzodiazepine agonists and antagonists but also by a new class of ligands which produce effects opposite to those of benzodiazepines, that is they produce convulsions and anxiety. These ligands can be described as having a negative efficacy at the receptor; tentatively they are named “inverse agonists”. Pharmacological experiments indicate that agonists, antagonists and inverse agonists comprise a whole continuum of agents with a graduated variety of efficacy at the receptor. Biochemical studies, supported by published electrophysiological data, indicate that the benzodiazepine receptor allosterically up- or down-regulates the gain in the GABAergic system depending on the nature of the ligand.

Expectations Equilibria with Dispersed Information: Existence with Approximate Rationality in a Model with a Continuum of Agents and Finitely Many States of the World

A model of a large economy in which prices transmit information (about the state of the world which is an argument in consumers' utility functions) from more informed to less informed agents is analysed. The basic hypothesis is that the forecast functions of imperfectly informed agents are suitably dispersed. For any such distribution of forecasts, market clearing prices exist. Moreover, there is always an equilibrium in which each agent's expectations are approximately rational.

Approximate equilibria in markets with indivisible commodities

This paper presents results on the existence of approximate equilibria in large but finite exchange economies in which all the traders have non-convex consumption sets. As such, the paper gives a natural extension, to the finite economy, of Mas-Colell's results on existence with indivisible commodities and a continuum of agents. It also presents an approximate equilibrium theorem without any assumption of compactness or bounded non-convexity of preferences.

Core and value for a public-goods economy: An example

An example of a public-goods economy with a continuum of agents is presented in which the Shapley value does not lie in the core.

Introduction to Equilibrium Analysis.

Advanced Textbooks in Economics, Volume 6: Introduction to Equilibrium Analysis: Variations on Themes by Edgeworth and Walras focuses on the approaches developed and instituted by Edgeworth and Walras in the study of equilibrium analysis. The book first underscores exchange economies, core of a game, and large economies. Discussions focus on economies with a continuum of agents, Walras equilibrium, prices and demand, balancedness, and commodity space. The manuscript then ponders on limit theorems for the core and existence of competitive equilibria. Topics include equilibria without convexity of preferences, existence of equilibria for economies with convex preferences, individual demand, emergence of prices, asymptotic equal treatment for most, uniform boundedness of core allocations, and limit theorems for type and replica economies. The publication examines continuous, upper, and lower hemi-continuous correspondences, fixed point theorems, and separation of convex sets. The book is a vital source of data for economists and researchers interested in equilibrium analysis.

Introduction to Equilibrium Analysis.

Advanced Textbooks in Economics, Volume 6: Introduction to Equilibrium Analysis: Variations on Themes by Edgeworth and Walras focuses on the approaches developed and instituted by Edgeworth and Walras in the study of equilibrium analysis. The book first underscores exchange economies, core of a game, and large economies. Discussions focus on economies with a continuum of agents, Walras equilibrium, prices and demand, balancedness, and commodity space. The manuscript then ponders on limit theorems for the core and existence of competitive equilibria. Topics include equilibria without convexity of preferences, existence of equilibria for economies with convex preferences, individual demand, emergence of prices, asymptotic equal treatment for most, uniform boundedness of core allocations, and limit theorems for type and replica economies. The publication examines continuous, upper, and lower hemi-continuous correspondences, fixed point theorems, and separation of convex sets. The book is a vital source of data for economists and researchers interested in equilibrium analysis.

Pareto Optimality in Non-Convex Economies

This article uses the concept of cone of interior displacements, which extends the notion of differentiability, to set up a characterization of Pareto optima in non-convex economies. A general theorem asserting that a Pareto optimum is a PA equilibrium is given and specifications are discussed. It is finally argued that the usual formulation of the doctrine of marginal cost pricingas a doctrine for achieving Pareto optimal states in a non-convex decentralized economy has unsatisfactory logical basis, and a way of defining a minimum degree of centralization inherent to non-convex economies is suggested. THE MAIN RESULTS of the economic theory of allocation of resources rest upon assumptions of convexity: convexity of production sets, and convexity of preferences. The relevance of these assumptions is often doubtful; even if in a many consumer economy the classical statements can be extended to the case of nonconvex preferences (this idea, pointed out first by Farrell [13] and Rothenberg [24], was developed in the general framework of economics with a continuum of agents as introduced by Aumann [4]; see W. Hildenbrand [18 and 19]), the indivisibilities arising in production are often large and create non-convexities that cannot be overlooked. Furthermore, non-convexities may arise with externalities (see Baumol [5], Kolm [20], and Starrett [25]), exchange of information (see Radner [23]), or stock markets (see Dreze [10]). Even if one must take the risk of producing less elegant results, a relevant economic theory cannot ignore non-convexities.

The Equality of the Core and the Set of Equilibria in Economies with Infinitely Many Commodities and a Continuum of Agents

IT IS BY NO MEANS CLEAR that Robert Aumann's Theorem on the equality of the core and the set of equilibria in atomless markets [1] applies to economies with infinitely many commodities. The existence of infinitely many commodities makes it possible for there to be an enormous variation in the characteristics of the agents in an economy. If these characteristics were sufficiently dispersed, it could be very hard to find a non-null set of agents with interests sufficiently similar or compatible to make it possible to form a blocking coalition. Thus, blocking coalitions could be so rare that almost all feasible allocations would be in the core. We show that suitable restrictions remove this difficulty and that Aumann's Theorem can be made to apply to economies whose commodity space is . (M, . p), the set of essentially bounded measurable functions on the measure space (M, ,//, pe). Our key restrictions are measurability assumptions about the maps defining agents' characteristics. Another way to restrict an economy in order to avoid the difficulty we have mentioned is to restrict the size of the commodity space. Jean Gabsewicz has shown that under very general assumptions, Aumann's Theorem applies to economies whose commodity space is C(S), the set of continuous functions on a compact metric space [6, (Chapter 5)]. The key property possessed by this space, from the point of view of size, is topological separability. A justification and explanation of the use of 9cO as a commodity space and of many of our assumptions may be found in [3]. In particular, we defend there the use of the Mackey topology for the duality (i2.c, 56). In Section 4 of this paper, we check that our model is internally consistent by proving that under certain acceptable assumptions, equilibria are measurable in the sense that we require of core allocations. Though consistent, our theory may be nearly empty, for only in a very special case have atomless markets with infinitely many commodities been shown to have equilibria [2, (Chapter 5)]. Jean-Francois Mertens has independently obtained results similar to our own.