Mathematical Methods of Game and Economic Theory

Klappentext This text begins with optimization theory and convex analysis, followed by topics in game theory and mathematical economics, and concluding with an introduction to nonlinear analysis and control theory. 1982 edition. Inhaltsverzeichnis Preface to the Dover EditionPreface (1982)Summary of ResultsContents of Other Possible CoursesNotationsI. Optimization and convex analysis1. Minimization problems and convexity2. Existence, uniqueness and stability of optimal solutions3. Compactness and continuity properties4. Differentiability and subdifferentiability: characterization of optimal solutions5. Introduction to duality theoryII. Game theory and the Walras model of allocation of resources6. Two-person games: an introduction7. Two-person zero-sum games: existence theorems8. The fundamental economic model: Walras equilibria9. Non-cooperative n-person games10. Main solution concepts of cooperative games11. Games with side-payments12. Games without side-paymentsIII. Non-linear analysis and optimal control theory13. Minimax type inequalities, monotone correspondences and gamma-convex functions14. Introduction to calculus of variations and optimal control15. Fixed point theorems, quasi-variational inequalities and correspondencesAppendix A. Summary of linear functional analysisAppendix B. The Knaster-Kuratowski-Mazurkiewicz lemmaAppendix C. Lyapunov's theorem on the range of a vector valued measureCommentsReferencesSubject index

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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