Mathematical Methods of Game and Economic Theory : Revised Edition - Aubin, Jean-Pierre

Mathematical Methods of Game and Economic Theory : Revised Edition

Jean-Pierre Aubin

Yayınevi: Dover Publications

Yayın tarihi: 11/2007

ISBN: 9780486462653

İngilizce | 656 Sayfa | 160 mm x 233 mm

Tür: Matematik-İstatistik

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This three-part 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. Jean-Pierre Aubin is theauthor of Dover's Approximation of Elliptic Boundary-Value Problemsand co-author of Applied Nonlinear Analysis. Reprint of the North-Holland Publishing Company, Amsterdam, 1982 edition.

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

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