Introduction to the theory of games

Description

Title page FOREWORD CHAPTER 1 RECTANGULAR GAMES 1. Introduction 2. Terminology, and Classification of Games 3. Definition of Rectangular Games 4. Rectangular Games with Saddle-points CHAPTER 2 THE FUNDAMENTAL THEOREM FOR RECTANGULAR GAMES 1. Mixed Strategies 2. Geometrical Background 3. Proof of the Fundamental Theorem for Arbitrary Rectangular Games 4. Properties of Optimal Strategies 5. Relations of Dominance 6. A Graphical Method of Solution CHAPTER 3 THE SOLUTIONS OF A RECTANGULAR GAME 1. The Set of Solutions 2. Some Properties of Matrices 3. The Determination of All Solutions CHAPTER 4 A METHOD OF APPROXIMATING THE VALUE OF A GAME CHAPTER 5 GAMES IN EXTENSIVE FORM 1. Normal Form and Extensive Form 2. Graphical Representation 3. Information Sets 4. Chance Moves 5. Games with More Than Two Players 6. Restrictions on Information Sets CHAPTER 6 GAMES IN EXTENSIVE FORM-GENERAL THEORY 1. General Definition of Finite Games 2. Games with Perfect Information-Equilibrium Points 3. Games with Perfect Recall, and Behavior Strategies CHAPTER 7 GAMES WITH INFINITELY MANY STRATEGIES CHAPTER 8 DISTRIBUTION FUNCTIONS 1. Intuitive Considerations 2. Formal Development CHAPTER 9 STIELTJES INTEGRALS CHAPTER 10 THE FUNDAMENTAL THEOREM FOR CONTINUOUS GAMES 1. The Value of a Continuous Game 2. Two Algebraic Lemmas 3. The Fundamental Theorem 4. Devices for Computing and Verifying Solutions CHAPTER 11 SEPARABLE GAMES 1. The Mappiog Method 2. An Illustrative Example 3. Fixed-points 4. Further Examples 5. Rectangular Game Solved as a Separable Game 6. Constrained Game Solved as a Separable Game CHAPTER 12 GAMES WITH CONVEX PAYOFF FUNCTIONS 1. Convex Functions 2. A Unique Strategy for One Player 3. Strategies for the Other Player 4. Remarks and an Example CHAPTER 13 APPLICATIONS TO STATISTICAL INFERENCE CHAPTER 14 LINEAR PROGRAMMING CHAPTER 15 ZERO-SUM n-PERSON GAMES 1. Characteristic Functions 2. Reduced Form CHAPTER 16 SOLUTIONS OF n-PERSON GAMES 1. Imputations 2. Definition of a Solution 3. Isomorphic Games 4. Three-person Games CHAPTER 17 GAMES WITHOUT ZERO-SUM RESTRICTION: THE VON NEUMANN-MORGENSTERN THEORY 1. Characteristic Functions 2. Imputations and Solutions CHAPTER 18 SOME OPEN PROBLEMS 1. Two Types of Problems 2. Games Played over Function Space 3. Pseudo-games 4. Non-zero-sum Games and n-Person Games BIBLIOGRAPHY INDEX