Mathematical Methods and Theory in Games, Programming, and Economics

Volume 2: The Theory of Infinite Games

Samuel Karlin, Z. W. Birnbaum

• Publisher: Pergamon
• Year: 2014
• Print ISBN:
  9781483198972
• eBook ISBN:
  9781483224008
• Topic: Matemáticas
• Subtopic: Matemática aplicada

Mathematical Methods and Theory in Games, Programming, and Economics, Volume II provides information pertinent to the mathematical theory of games of strategy. This book presents the mathematical tools for manipulating and analyzing large sets of strategies. Organized into nine chapters, this volume begins with an overview of the fundamental concepts in game theory, namely, strategy and pay-off. This text then examines the identification of strategies with points in Euclidean n-space, which is a convenience that simplifies the mathematical analysis. Other chapters provide a discussion of the theory of finite convex games. This book discusses as well the extension of the theory of convex continuous games to generalized convex games, which leads to the characterization that such games possess optimal strategies of finite type. The final chapter deals with the components of a simple two-person poker game. This book is a valuable resource for mathematicians, statisticians, economists, social scientists, and research workers.

Table of contents

• Front Cover
• Mathematical Methods and Theory in Games, Programming, and Economics
• Copyright Page
• Table of Contents
• CHAPTER 1. THE DEFINITION OF A GAME AND THE MIN-MAX THEOREM
• CHAPTER 2. THE NATURE AND STRUCTURE OF INFINITE GAMES
• CHAPTER 3. SEPARABLE AND POLYNOMIAL GAMES
• CHAPTER 4. GAMES WITH CONVEX KERNELS AND GENERALIZED CONVEX KERNELS
• CHAPTER 5. GAMES OF TIMING OF ONE ACTION FOR EACH PLAYER
• CHAPTER 6. GAMES OF TIMING (CONTINUED)
• CHAPTER 7. MISCELLANEOUS GAMES
• CHAPTER 8. INFINITE CLASSICAL GAMES NOT PLAYED OVER THE UNIT SQUARE
• CHAPTER 9. POKE R AND GENERAL PARLOR GAMES
• SOLUTIONS TO PROBLEMS
• APPENDIX A. VECTOR SPACES AND MATRICES
• APPENDIX B. CONVEX SETS AND CONVEX FUNCTIONS
• APPENDIX C. MISCELLANEOUS TOPICS
• BIBLIOGRAPHY
• INDEX