Optima and Equilibria
Subtitle: An Introduction to Nonlinear Analysis
By: by Jean-Pierre Aubin
Edition: Second Edition.
Series: Graduate Texts in Mathematics -- 140
Publisher: Springer Berlin Heidelberg; Imprint: Springer
Published: 1998
Place of publication: Berlin, Heidelberg
Language: eng
Number of pages: 437
ISBN-13: 9783662035399; 9783642084461
Subjects: Economics; Mathematics; System theory; Global analysis (Mathematics); Mathematical optimization; Operations research; Analysis; Control Systems Theory; Calculus of Variations and Optimal Control; Optimization; Operation Research/Decision Theory
Description: 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)
Table of contents: title: Part I Nonlinear Analysis: Theory: Minimisation Problems: General theorems; title: Convex Functions and Proximation, Projection and Separation Theorems; title: Conjugate Functions and Convex Minimisation Problems; title: Subidfferentials of Convex Functions; title: Marginal Properties of Solutions od Convex Minimisation; title: Generalised Gradients of Locally Lipschitz Functions; title: Two-person Games. Fundamental Concepts and Examples; title: Two-person Zero-sum Games: Theorems of Von Neumann and Ky Fan; title: Solution of Nonlinear Equations and Inclusions; title: Introduction to the Theory of Economic Equilibrium; title: The Von Neumann Growth Model; title: n-person Games; title: Cooperative Games and Fuzzy Games; title: Part II Nonlinear Analysis: Examples: Exercises; title: Statements of Problems; title: Solutions to Problems Appendix: Compendium of Resluts; title: References; title: Index.