CHAPTER 1 RECTANGULAR GAMES 1
1．Introduction 1
2．Terminology,and Classification of Games 3
3．Definition of Rectangular Games 6
4．Rectangular Games with Saddle-points 8
CHAPTER 2 THE FUNDAMENTAL THEOREM FOR RECTANGULAR GAMES 21
1．Mixed Strategies 21
2．Geometrical Background 25
3．Proof of the Fundamental Theorem for Arbitrary Rectangular Games 31
4．Properties of Optimal Strategies 37
5．Relations of Dominance 46
6．A Graphical Method of Solution 52
CHAPTER 3 THE SOLUTIONS OF A RECTANGULAR GAME 59
1．The Set of Solutions 59
2．Some Properties of Matrices 61
3．The Determination of All Solutions 67
CHAPTER 4 A METHOD OF APPROXIMATING THE VALUE OF A GAME 89
CHAPTER 5 GAMES IN EXTENSIVE FORM 97
1．Normal Form and Extensive Form 97
2．Graphical Representation 101
3．Information Sets 103
4．Chance Moves 108
5．Games with More Than Two Players 112
6．Restrictions on Information Sets 114
CHAPTER 6 GAMES IN EXTENSIVE FORM—GENERAL THEORY 119
1．General Definition of Finite Games 119
2．Games with Perfect Information—Equilibrium Points 125
3．Games with Perfect Recall,and Behavior Strategies 134
CHAPTER 7 GAMES WITH INFINITELY MANY STRATEGIES 141
CHAPTER 8 DISTRIBUTION FUNCTIONS 151
1．Intuitive Considerations 151
2．Formal Development 157
CHAPTER 9 STIELTJES INTEGRALS 167
CHAPTER 10 THE FUNDAMENTAL THEOREM FOR CONTINUOUS GAMES 183
1．The Value of a Continuous Game 183
2．Two Algebraic Lemmas 184
3．The Fundamental Theorem 186
4．Devices for Computing and Verifying Solutions 193
CHAPTER 11 SEPARABLE GAMES 219
1．The Mapping Method 219
2．An Illustrative Example 230
3．Fixed-points 237
4．Further Examples 244
5．Rectangular Game Solved as a Separable Game 251
6．Constrained Game Solved as a Separable Game 254
CHAPTER 12 GAMES WITH CONVEX PAYOFF FUNCTIONS 259
1．Convex Functions 259
2．A Unique Strategy for One Player 262
3．Strategies for the Other Player 266
4．Remarks and an Example 270
CHAPTER 13 APPLICATIONS TO STATISTICAL INFERENCE 277
CHAPTER 14 LINEAR PROGRAMMING 291
CHAPTER 15 ZERO-SUM n-PERSON GAMES 303
1．Characteristic Functions 303
2．Reduced Form 313
CHAPTER 16 SOLUTIONS OF n-PERSON GAMES 325
1．Imputations 325
2．Definition of a Solution 329
3．Isomorphic Games 332
4．Three-person Games 335
CHAPTER 17 GAMES WITHOUT ZERO-SUM RESTRICTION:THE VON NEUMANN-MORGENSTERN THEORY 343
1．Characteristic Functions 343
2．Imputations and Solutions 348
CHAPTER 18 SOME OPEN PROBLEMS 355
1．Two Types of Problems 355
2．Games Played over Function Space 355
3．Pseudo-games 357
4．Non-zero-sum Games and n-Person Games 358
BIBLIOGRAPHY 361
INDEX 369