Equilibrium Theory in Infinite Dimensional Spaces

1. Front Matter

   Pages i-x

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2. Mathematical Background

   1. Front Matter

      Pages 1-1

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   2. Integration of Banach-Valued Correspondence

      • Nicholas C. Yannelis

      Pages 2-35

   3. Set-Valued Functions of Two Variables in Economic Theory

      • Nicholas C. Yannelis

      Pages 36-72

3. Equilibria, Core, and Pareto Optimality

   1. Front Matter

      Pages 73-73

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   2. A Theorem on the Existence of Competitive Equilibria in a Market with a Finite Number of Agents and Whose Commodity Space is L∞

      • Truman F. Bewley

      Pages 74-101

   3. The Core of an Economy Without Ordered Preferences

      • Nicholas C. Yannelis

      Pages 102-123

   4. Fundamental Theorems of Welfare Economics in Infinite Dimensional Commodity Spaces

      • Robert A. Becker

      Pages 124-175

4. Core Equivalence

   1. Front Matter

      Pages 177-177

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   2. A Limit Theorem on the Core of an Economy with a Continuum of Commodities

      • Jean Jaskold Gabszewicz

      Pages 178-188

   3. An Equivalence Theorem for the Core of an Economy with Commodity Space L_∞ — τ (L_∞ ,L₁)

      • Jean-François Mertens

      Pages 189-196

   4. The Principle of Equivalence

      • Harrison H. C. Cheng

      Pages 197-221

5. The Existence of an Equilibrium in Economies with a Continuum of Agents

   1. Front Matter

      Pages 223-223

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   2. A Very Weak Theorem on the Existence of Equilibria in Atomless Economies with Infinitely Many Commodities

      • Truman F. Bewley

      Pages 224-232

   3. Equilibria in Markets with a Continuum of Agents and Commodities

      • M.Ali Khan, Nicholas C. Yannelis

      Pages 233-248

   4. What is Perfect Competition?

      • Aldo Rustichini, Nicholas C. Yannelis

      Pages 249-265

6. Correlated Equilibria

   1. Front Matter

      Pages 267-267

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   2. On the Existence of Correlated Equilibria

      • Nicholas C. Yannelis, Aldo Rustichini

      Pages 268-280

   3. Existence of Correlated Weak Equilibria in Discontinuous Games

      • Andrzej S. Nowak

      Pages 281-287

   4. Communication Equilibria with Large State Spaces

      • Kevin D. Cotter

      Pages 288-299

Apart from the underlying theme that all the contributions to this volume pertain to models set in an infinite dimensional space, they differ on many counts. Some were written in the early seventies while others are reports of ongoing research done especially with this volume in mind. Some are surveys of material that can, at least at this point in time, be deemed to have attained a satisfactory solution of the problem, while oth­ ers represent initial forays into an original and novel formulation. Some furnish alternative proofs of known, and by now, classical results, while others can be seen as groping towards and exploring formulations that have not yet reached a definitive form. The subject matter also has a wide leeway, ranging from solution concepts for economies to those for games and also including representation of preferences and discussion of purely mathematical problems, all within the rubric of choice variables belonging to an infinite dimensional space, interpreted as a commodity space or as a strategy space. Thus, this is a collective enterprise in a fairly wide sense of the term and one with the diversity of which we have interfered as little as possible. Our motivation for bringing all of this work under one set of covers was severalfold.

• Gleichgewichtstheorie
• Infinite Dimensional Commodity Space
• Nash Gleichgewicht
• Walras Gleichgewicht
• Walrasian Equilibrium
• agents

• The Johns Hopkins University, Baltimore, USA

  M. Ali Khan

• Department of Economics, University of Illinois at Urbana-Champaign, Champaign, USA

  Nicholas C. Yannelis

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