Equilibrium Theory in Infinite Dimensional Spaces

✍ Scribed by Nicholas C. Yannelis (auth.), Prof. Dr. M. Ali Khan, Prof. Dr. Nicholas C. Yannelis (eds.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 1991
• Tongue: English
• Leaves: 441
• Series: Studies in Economic Theory 1
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-x
Front Matter....Pages 1-1
Integration of Banach-Valued Correspondence....Pages 2-35
Set-Valued Functions of Two Variables in Economic Theory....Pages 36-72
Front Matter....Pages 73-73
A Theorem on the Existence of Competitive Equilibria in a Market with a Finite Number of Agents and Whose Commodity Space is L ∞ ....Pages 74-101
The Core of an Economy Without Ordered Preferences....Pages 102-123
Fundamental Theorems of Welfare Economics in Infinite Dimensional Commodity Spaces....Pages 124-175
Front Matter....Pages 177-177
A Limit Theorem on the Core of an Economy with a Continuum of Commodities....Pages 178-188
An Equivalence Theorem for the Core of an Economy with Commodity Space L ∞ — τ (L ∞ ,L 1 )....Pages 189-196
The Principle of Equivalence....Pages 197-221
Front Matter....Pages 223-223
A Very Weak Theorem on the Existence of Equilibria in Atomless Economies with Infinitely Many Commodities....Pages 224-232
Equilibria in Markets with a Continuum of Agents and Commodities....Pages 233-248
What is Perfect Competition?....Pages 249-265
Front Matter....Pages 267-267
On the Existence of Correlated Equilibria....Pages 268-280
Existence of Correlated Weak Equilibria in Discontinuous Games....Pages 281-287
Communication Equilibria with Large State Spaces....Pages 288-299
Front Matter....Pages 301-301
An Axiomatic Approach to the Efficiency of Non-Cooperative Equilibrium in Economies with a Continuum of Traders....Pages 302-324
On Symmetric Cournot-Nash Equilibrium Distributions in a Finite-Action, Atomless Game....Pages 325-332
Equilibria in Random and Bayesian Games with a Continuum of Players....Pages 333-350
Front Matter....Pages 351-351
Recursive Utility Under Uncertainty....Pages 352-369
Consistency and Continuity of Choice in a Sequence of Spot and Futures Markets....Pages 370-417
Back Matter....Pages 419-437

✦ Subjects

Economic Theory