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

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

 

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.

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

Product Details

ISBN:
9783642084461
Author:
Aubin, Jean-pierre
Publisher:
Springer
Author:
Aubin, Jean-Pierre
Author:
Wilson, S.
Location:
Berlin, Heidelberg
Subject:
Mathematical Analysis
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-Analysis General
Subject:
Operation Research/Decision Theory
Subject:
Mathematics
Subject:
Language, literature and biography
Subject:
mathematics and statistics
Subject:
Global analysis (Mathematics)
Subject:
Economics
Subject:
Systems theory.
Subject:
Mathematical optimization
Subject:
Operations Research
Copyright:
Edition Description:
Softcover reprint of hardcover 2nd ed. 1998
Series:
Graduate Texts in Mathematics
Series Volume:
140
Publication Date:
20101207
Binding:
TRADE PAPER
Language:
English
Pages:
454
Dimensions:
235 x 155 mm 682 gr

Related Subjects

Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » Computer
Science and Mathematics » Mathematics » Set Theory
Science and Mathematics » Physics » General

Graduate Texts in Mathematics #140: Optima and Equilibria: An Introduction to Nonlinear Analysis New Trade Paper
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Product details 454 pages Springer - English 9783642084461 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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