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 Mapping 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