Mathematical Methods of Game and Economic Theory Revised Edition

by Aubin, Jean-Pierre

• ISBN13: 9780486789354
• ISBN10: 0486789357
• Format: Hardcover
• Copyright: 2013-12-23
• Publisher: Dover Publications

Summary

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.

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