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Optima and Equilibria: An Introduction to Nonlinear Analysis

Optima and Equilibria: An Introduction to Nonlinear Analysis
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Field name Details
Dewey Class 515.7
Title Optima and Equilibria ([EBook] :) : An Introduction to Nonlinear Analysis / / by Jean-Pierre Aubin.
Author Aubin, Jean-Pierre
Other name(s) SpringerLink (Online service)
Edition statement Second Edition.
Publication Berlin, Heidelberg : : Springer Berlin Heidelberg : : Imprint: Springer, , 1998.
Physical Details XVII, 433 p. : online resource.
Series Graduate texts in mathematics 0072-5285 ; ; 140
ISBN 9783662035399
Summary Note 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).:
Contents note 1 Minimisation Problems: General Theorems -- 2 Convex Functions and Proximation, Projection and Separation Theorems -- 3 Conjugate Functions and Convex Minimisation Problems -- 4 Subdifferentials of Convex Functions -- 5 Marginal Properties of Solutions of Convex Minimisation Problems -- 6 Generalised Gradients of Locally Lipschitz Functions -- 7 Two-person Games. Fundamental Concepts and Examples -- 8 Two-person Zero-sum Games: Theorems of Von Neumann and Ky Fan -- 9 Solution of Nonlinear Equations and Inclusions -- 10 Introduction to the Theory of Economic Equilibrium -- 11 The Von Neumann Growth Model -- 12 n-person Games -- 13 Cooperative Games and Fuzzy Games -- 14 Exercises -- 15 Statements of Problems -- 16 Solutions to Problems -- 17 Compendium of Results -- References.
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