Fixed Points And Economic Equilibria

By: Ken Urai

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Hardcover | 21 May 2010

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312 Pages

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22.86 x 15.24 x 1.91

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This book presents a systematic approach to problems in economic equilibrium based on fixed-point arguments and rigorous set-theoretical (axiomatic) methods. It describes the highest-level research on the classical theme, fixed points and economic equilibria, in the theory of mathematical economics, and also presents basic results in this area, especially in the general equilibrium theory and non-co-operative game theory. The arguments also contain distinguishable developments of the main theme in the homology theory for general topological spaces, in the model theory and mathematical logic, and in the methodology and philosophy of social sciences. It can thus serve as a graduate-level textbook on mathematical economics as well as an advanced monograph for students and researchers who are concerned about rigorous mathematical treatment in the social sciences.

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You Can Find This Book In

Non-Fiction Economics Economic Theory & Philosophy Mathematics Applied Mathematics Optimisation Game Theory Business & Management Business Mathematics & Systems Mathematical Foundation Mathematical Logic Booktopia Publisher Services

World Scientific Publishing

Preface	p. vii
Introduction	p. 1
Mathematics is Language	p. 1
Notes on Some Mathematical Tools in This Book	p. 2
Basic Mathematical Concepts and Definitions	p. 12
Fixed-Point Theorems	p. 27
Classical Results and Basic Extensions	p. 27
Convexity and Duality for General Spaces	p. 39
Extension of Classical Results to General Spaces	p. 46
Nash Equilibrium and Abstract Economy	p. 57
Multi-Agent Product Settings for Games	p. 57
Nash Equilibrium	p. 67
Abstract Economy	p. 75
Gale-Nikaido-Debreu's Theorem	p. 87
Gale-Nikaido-Debreu's Theorem	p. 87
Market Equilibria in General Vector Spaces	p. 91
Demand-Supply Coincidence in General Spaces	p. 99
General Economic Equilibrium	p. 101
General Preferences and Basic Existence Theorems	p. 101
Pareto Optimal Allocations	p. 109
Existence of General Equilibrium	p. 111
The Cech Type Homology Theory and Fixed Points	p. 125
Basic Concepts in Algebraic Topology	p. 125
Vietoris-Begle Mapping and Local Connectedness	p. 142
Nikaido's Analogue of Sperner's Lemma	p. 150
eilenberg-Montgomery's Theorem	p. 164
Convex Structure and Fixed-Point Index	p. 167
Lefschetz's Fixed-Point Theorem and Its Extensions	p. 167
Cohomology Theory for General Spaces	p. 175
Dual-System Structure and Differentiability	p. 177
Linear Approximation for Isolated Fixed Points	p. 177
Indices for Compact Set of Fixed Points	p. 180
Applications to Related Topics	p. 183
KKM, KKMS, and Core Existence	p. 183
Eaves' Theorem	p. 187
Fan-Browder's Coincidence Theorem	p. 189
L-majorized Mappings	p. 190
Variational Inequality Problem	p. 191
Equilibrium with Cooperative Concepts	p. 192
System of Inequalities and Affine Transformations	p. 195
Mathematics and Social Science	p. 201
Basic Concepts in Axiomatic Set Theory	p. 201
Individuals and Rationality	p. 218
Society and Values	p. 232
Concluding Discussions	p. 243
Fixed Points and Economic Equilibria	p. 243
Rationality and Fixed-Point Views of the World	p. 250
	p. 257
	p. 263
	p. 273
References	p. 277
Index	p. 285
Table of Contents provided by Ingram. All Rights Reserved.

Fixed Points And Economic Equilibria

At a Glance

Hardcover

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