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AuthorAubin, Jean-Pierre. author
TitleOptima and Equilibria [electronic resource] : An Introduction to Nonlinear Analysis / by Jean-Pierre Aubin
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1998
Edition Second Edition
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Descript XVII, 433 p. online resource


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)


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

Mathematics Mathematical analysis Analysis (Mathematics) Functional analysis Applied mathematics Engineering mathematics System theory Calculus of variations Economic theory Mathematics Functional Analysis Applications of Mathematics Analysis Economic Theory/Quantitative Economics/Mathematical Methods Systems Theory Control Calculus of Variations and Optimal Control; Optimization


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