Description
Book SynopsisOffers an introduction to the mathematical discipline known as the Theory of Games. This book opens by addressing 'matrix games'. It continues with a treatment of games in extensive form and also deals with games that have an infinite number of pure strategies for the two players. It features examples and exercises, and various historical notes.
Table of ContentsAuthor's Note vii Preface ix Chapter 1. What Is the Theory of Games? 1 Notes 3 Chapter 2. Matrix Games 5 2.1 Two Examples 5 2.2 The Definition of a Matrix Game 9 2.3 The Fundamental Theorem for 2 x 2 Matrix Games 10 2.4 The Geometry of Convex Sets 12 2.5 Fundamental Theorem for All Matrix Games 21 2.6 A Graphical Method of Solution 24 2.7 An Algorithm for Solving All Matrix Games 28 2.8 Simplified Poker 36 Notes 45 Appendix 48 Chapter 3. Extensive Games 59 3.1 Some Preliminary Restrictions 59 3.2 The Axiom System 59 3.3 Pure and Mixed Strategies 64 3.4 Games with Perfect Information 66 3.5 A Reduction of the Game Matrix 67 3.6 An Instructive Example 70 3.7 Behavior Strategies and Perfect Recall 72 3.8 Simplified Poker Reconsidered 77 Notes 78 Chapter 4. Infinite Games 81 4.1 Some Preliminary Restrictions 81 4.2 An Illuminating Example 81 4.3 Mixed Strategies and Expectation 83 4.4 The Battle of the Maxmin versus Supinf 88 4.5 The Fundamental Theorem 92 4.6 The Solution of Games on the Unit Square 94 Notes 103 Index 105
