Mathematical Methods of Game and Economic Theory (Volume 7) (Studies in Mathematics and its Applications, Volume 7)

This book presents a unified treatment of optimization theory, game theory and a general equilibrium theory in economics in the framework of nonlinear functional analysis. It not only provides powerful and versatile tools for solving specific problems in economics and the social sciences but also serves as a unifying theme in the mathematical theory of these subjects as well as in pure mathematics itself. 05 Preface 06 Summary of Results - A Guideline for the Reader 07 Contents of Other Possible Courses 08 Notations 09 Chapter 1 Minimization Problems and Convexity 10 Chapter 2 Existence, Uniqueness and Stability of Optimal Solutions 11 Chapter 3 Compactness and Continuity Properties 12 Chapter 4 Differentiability and Subdifferentiability - Characterization of Optimal Solutions 13 Chapter 5 Introduction to Duality Theory 14 Chapter 6 Two-Person Games - An Introduction 15 Chapter 7 Two-Person Zero-Sum Games - Existence Theorems 16 Chapter 8 The Fundamental Economic Model - Walras Equilibria 17 Chapter 9 Non-Cooperative n-Person Games 18 Chapter 10 Main Solution Concepts of Cooperative Games 19 Chapter 11 Games with Side-Payments 20 Chapter 12 Games without Side-Payments 22 Chapter 14 Introduction to Calculus of Variations and Optimal Control 23 Chapter 15 Fixed Point Theorems, Quasi-Variational Inequalities and Correspondences 24 Appendix A Summary of Linear Functional Analysis 25 Appendix B The Knaster-Kuratowski-Mazurkiewicz Lemma 26 Appendix C Lyapunov's Theorem on the Range of a Vector Valued Measure 27 Comments 28 References 29 Subject Index