Optima and Equilibria: An Introduction to Nonlinear Analysis: Vol 140 (Graduate Texts in Mathematics) - Hardcover

Aubin, J.P.

Hardcover

ISBN 10: 3540521216 ISBN 13: 9783540521211

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1993

Synopsis

Progress in the theory of economic equilibria and 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 yet 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, co-operative and non-co-operative games, fuzzy games, etc. It begins with the foundations of optimization theory and mathematical programming, in particular convex and non-smooth analysis. Nonlinear analysis is presented, first game-theoretically, and then in the framework of set valued analysis. These results are then applied to the main classes of economic equilibria. The text continues with game theory, non-co-operative (Nash) equilibria, Pareto optima and finally some fuzzy game theory. The book closes with numerous exercises and problems.

About this title

Review

From the reviews: MATHEMATICAL REVIEWS" provides a concise and self-contained exposition of the fundamental results both in the theory and its applications Overall, the book presents a fundamental introduction to nonlinear analysis and its economic and game-theoretic applications. It can serve as a basic textbook for students and researchers interested in these areas."

From the Back Cover

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)

Edition details

• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Publication date: 1993
• Language: English
• ISBN 10: 3540521216
• ISBN 13: 9783540521211
• Binding: Hardcover
• Number of pages: 415