Author(s): J.C.C. McKinsey
Publisher: RAND
Year: 1952
Language: English
Commentary: complete
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
