Equilibrium Theory in Infinite Dimensional Spaces: (1 Studies in Economic Theory)

The purpose of this monograph is to study several solution concepts such as the Walrasian Equilibrium, the Pareto opti- mality, the Core, the Nash Equilibrium and the Correlated equilibrium in the context of an infinite dimensional commodity or strategy space. Of course, the study of the above equilibrium notions in an infinite dimensional commodity or strategy space not only requires novel technical arguments and a modification and correction of much of our finite-dimensional intuition about these concepts, but this point also goes the other way; a successful formulation of the outstanding questions has also necessitated the creation of new mathematics. Some of the contributions in this volume also present a flavor of these technical advances that have been made in the last twenty years.

Table of Contents:
1 Mathematical Background.- Integration of Banach-Valued Correspondences.- Set-Valued Functions of Two Variables in Economic Theory.- 2 Equilibria, Core, and Pareto Optimality.- A Theorem on the Existence of Competitive Equilibria in a Market with a Finite Number of Agents and Whose Commodity Space is L?.- The Core of an Economy Without Ordered Preferences.- Fundamental Theorems of Welfare Economics in Infinite Dimensional Commodity Spaces.- 3 Core Equivalence.- A Limit Theorem on the Core of an Economy with a Continuum of Commodities.- An Equivalence Theorem for the Core of an Economy with Commodity Space L? ? ?(L?, L1).- The Principle of Equivalence.- 4 The Existence of an Equilibrium in Economies with a Continuum of Agents.- A Very Weak Theorem on the Existence of Equilibria in Atomless Economies with Infinitely Many Commodities.- Equilibria in Markets with a Continuum of Agents and Commodities.- What is Perfect Competition?.- 5 Correlated Equilibria.- On the Existence of Correlated Equilibria.- Existence of Correlated Weak Equilibria in Discontinuous Games.- Communication Equilibria with Large State Spaces.- 6 Games with a Continuum of Players.- An Axiomatic Approach to the Efficiency of Non-Cooperative Equilibrium in Economies with a Continuum of Traders.- On Symmetric Cournot-Nash Equilibrium Distributions in a Finite-Action, Atomless Game.- Equilibria in Random and Bayesian Games with a Continuum of Players.- 7 Sequential Equilibria.- Recursive Utility Under Uncertainty.- Consistency and Continuity of Choice in a Sequence of Spot and Futures Markets.- 8 References.