Publisher Description

Mathematical economics and game theory approached with the fundamental mathematical toolbox of nonlinear functional analysis are the central themes of this text. Both optimization and equilibrium theories are covered in full detail. The book's central application is the fundamental economic problem of allocating scarce resources among competing agents, which leads to considerations of the interrelated applications in game theory and the theory of optimization. Mathematicians, mathematical economists, and operations research specialists will find that it provides a solid foundation in nonlinear functional analysis.This text begins by developing linear and convex analysis in the context of optimization theory. The treatment includes results on the existence and stability of solutions to optimization problems as well as an introduction to duality theory. The second part explores a number of topics in game theory and mathematical economics, including two-person games, which provide the framework to study theorems of nonlinear analysis. The text concludes with an introduction to non-linear analysis and optimal control theory, including an array of fixed point and subjectivity theorems that offer powerful tools in proving existence theorems.

Author Biography

Aubin, University of Paris-Dauphine, France.

Table of Contents

Preface to the Dover Edition Preface (1982) Summary of Results Contents of Other Possible Courses Notations I. Optimization and convex analysis 1. Minimization problems and convexity 2. Existence, uniqueness and stability of optimal solutions 3. Compactness and continuity properties 4. Differentiability and subdifferentiability: characterization of optimal solutions 5. Introduction to duality theory II. Game theory and the Walras model of allocation of resources 6. Two-person games: an introduction 7. Two-person zero-sum games: existence theorems 8. The fundamental economic model: Walras equilibria 9. Non-cooperative n-person games 10. Main solution concepts of cooperative games 11. Games with side-payments 12. Games without side-payments III. Non-linear analysis and optimal control theory 13. Minimax type inequalities, monotone correspondences and gamma-convex functions 14. Introduction to calculus of variations and optimal control 15. Fixed point theorems, quasi-variational inequalities and correspondences Appendix A. Summary of linear functional analysis Appendix B. The Knaster-Kuratowski-Mazurkiewicz lemma Appendix C. Lyapunov's theorem on the range of a vector valued measure Comments References Subject index

Long Description

Mathematical economics and game theory approached with the fundamental mathematical toolbox of nonlinear functional analysis are the central themes of this text. Its central application is the fundamental economic problem of allocating scarce resources among competing agents, which leads to considerations of the interrelated applications in game theory and the theory of optimization. 1982 edition.

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