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Graduate Texts in Mathematics, #140: Optima and Equilibria: An Introduction to Nonlinear Analysis

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Synopses & Reviews

Publisher Comments:

Advances in game theory and economic theory have proceeded hand in hand with that of nonlinear analysis and in particular, convex analysis. These theories motivated mathematicians to provide mathematical tools to deal with optima and equilibria. Jean-Pierre Aubin, one of the leading specialists in nonlinear analysis and its applications to economics and game theory, has written a rigorous and concise-yet still elementary and self-contained- text-book to present mathematical tools needed to solve problems motivated by economics, management sciences, operations research, cooperative and noncooperative games, fuzzy games, etc. It begins with convex and nonsmooth analysis,the foundations of optimization theory and mathematical programming. Nonlinear analysis is next presented in the context of zero-sum games and then, in the framework of set-valued analysis. These results are applied to the main classes of economic equilibria. The text continues with game theory: noncooperative (Nash) equilibria, Pareto optima, core and finally, fuzzy games. The book contains numerous exercises and problems: the latter allow the reader to venture into areas of nonlinear analysis that lie beyond the scope of the book and of most graduate courses. -(See cont. News remarks)

Synopsis:

This book offers a self-contained, rigorous and concise review of the mathematical tools needed to study optima and equilibria, as solutions to problems in economics, management sciences, operations research, cooperative and non-cooperative games and more.

Synopsis:

Progress in the theory of economic equilibria and in game theory has proceeded hand in hand with that of the mathematical tools used in the field, namely nonlinear analysis and, in particular, convex analysis. Jean-Pierre Aubin, one of the leading specialists in nonlinear analysis and its application to economics, has written a rigorous and concise - yet still elementary and self-contained - textbook providing the mathematical tools needed to study optima and equilibria, as solutions to problems, arising in economics, management sciences, operations research, cooperative and non-cooperative games, fuzzy games etc. It begins with the foundations of optimization theory, and mathematical programming, and in particular convex and nonsmooth analysis. Nonlinear analysis is then presented, first game-theoretically, then in the framework of set valued analysis. These results are then applied to the main classes of economic equilibria. The book contains numerous exercises and problems: the latter allow the reader to venture into areas of nonlinear analysis that lie beyond the scope of the book and of most graduate courses.

Description:

Includes bibliographical references (p. [421]-424) and index.
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Table of Contents

Part I Nonlinear Analysis: Theory: Minimisation Problems: General theorems.- Convex Functions and Proximation, Projection and Separation Theorems.- Conjugate Functions and Convex Minimisation Problems.- Subidfferentials of Convex Functions.- Marginal Properties of Solutions od Convex Minimisation.- Generalised Gradients of Locally Lipschitz Functions.- Two-person Games. Fundamental Concepts and Examples.- Two-person Zero-sum Games: Theorems of Von Neumann and Ky Fan.- Solution of Nonlinear Equations and Inclusions.- Introduction to the Theory of Economic Equilibrium.- The Von Neumann Growth Model.- n-person Games.- Cooperative Games and Fuzzy Games.- Part II Nonlinear Analysis: Examples: Exercises.- Statements of Problems.- Solutions to Problems Appendix: Compendium of Resluts.- References.- Index

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Product Details

ISBN:
9783540649830
Translator:
Wilson, S.
Author:
Wilson, S.
Translator:
Wilson, Rosalee
Author:
Aubin, Jean-Pierre
Publisher:
Springer
Location:
Berlin ;
Subject:
General
Subject:
Mathematical Analysis
Subject:
Applied
Subject:
Economics
Subject:
Economics, mathematical
Subject:
Game Theory
Subject:
Nonlinear theories
Subject:
Equilibrium
Subject:
Fermat rule
Subject:
Fuzzy Games
Subject:
Nash
Subject:
OPTIMIZATION
Subject:
Pareto
Subject:
Walras
Subject:
Convex Analysis
Subject:
cooperative and non cooperative games
Subject:
Economic models
Subject:
minimax
Subject:
nonlinear analysis
Subject:
Nonsmooth analysis
Subject:
positive eigenvalues and eigenvectors
Subject:
subgradients
Subject:
von Neumann
Subject:
Zero-Sum-Games
Subject:
Analysis
Subject:
Economic theory
Subject:
Systems Theory, Control
Subject:
Calculus of Variations and Optimal Control; Optimization
Subject:
Operations Research/Decision Theory
Subject:
Mathematics-Applied
Subject:
ope
Subject:
rations Research/Decision Theory
Subject:
Operation Research/Decision Theory
Copyright:
1998
Edition Number:
2
Edition Description:
1998. Corr. 2nd
Series:
Graduate Texts in Mathematics,
Series Volume:
140
Publication Date:
20021118
Binding:
HARDCOVER
Language:
English
Illustrations:
Yes
Pages:
454
Dimensions:
235 x 155 mm 1810 gr
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Graduate Texts in Mathematics, #140: Optima and Equilibria: An Introduction to Nonlinear Analysis New Hardcover
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Product details 454 pages Springer-Verlag - English 9783540649830 Reviews:
"Synopsis" by , This book offers a self-contained, rigorous and concise review of the mathematical tools needed to study optima and equilibria, as solutions to problems in economics, management sciences, operations research, cooperative and non-cooperative games and more.
"Synopsis" by , Progress in the theory of economic equilibria and in game theory has proceeded hand in hand with that of the mathematical tools used in the field, namely nonlinear analysis and, in particular, convex analysis. Jean-Pierre Aubin, one of the leading specialists in nonlinear analysis and its application to economics, has written a rigorous and concise - yet still elementary and self-contained - textbook providing the mathematical tools needed to study optima and equilibria, as solutions to problems, arising in economics, management sciences, operations research, cooperative and non-cooperative games, fuzzy games etc. It begins with the foundations of optimization theory, and mathematical programming, and in particular convex and nonsmooth analysis. Nonlinear analysis is then presented, first game-theoretically, then in the framework of set valued analysis. These results are then applied to the main classes of economic equilibria. The book contains numerous exercises and problems: the latter allow the reader to venture into areas of nonlinear analysis that lie beyond the scope of the book and of most graduate courses.
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