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Introduction To The Theory of Games【2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载】

Introduction To The Theory of Games
  • J.C.C.McKinsey 著
  • 出版社： Inc.
  • ISBN：
  • 出版时间：1952
  • 标注页数：371页
  • 文件大小：43MB
  • 文件页数：383页
  • 主题词：

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图书目录

CHAPTER 1 RECTANGULAR GAMES1

1．Introduction1

2．Terminology,and Classification of Games3

3．Definition of Rectangular Games6

4．Rectangular Games with Saddle-points8

CHAPTER 2 THE FUNDAMENTAL THEOREM FOR RECTANGULAR GAMES21

1．Mixed Strategies21

2．Geometrical Background25

3．Proof of the Fundamental Theorem for Arbitrary Rectangular Games31

4．Properties of Optimal Strategies37

5．Relations of Dominance46

6．A Graphical Method of Solution52

CHAPTER 3 THE SOLUTIONS OF A RECTANGULAR GAME59

1．The Set of Solutions59

2．Some Properties of Matrices61

3．The Determination of All Solutions67

CHAPTER 4 A METHOD OF APPROXIMATING THE VALUE OF A GAME89

CHAPTER 5 GAMES IN EXTENSIVE FORM97

1．Normal Form and Extensive Form97

2．Graphical Representation101

3．Information Sets103

4．Chance Moves108

5．Games with More Than Two Players112

6．Restrictions on Information Sets114

CHAPTER 6 GAMES IN EXTENSIVE FORM—GENERAL THEORY119

1．General Definition of Finite Games119

2．Games with Perfect Information—Equilibrium Points125

3．Games with Perfect Recall,and Behavior Strategies134

CHAPTER 7 GAMES WITH INFINITELY MANY STRATEGIES141

CHAPTER 8 DISTRIBUTION FUNCTIONS151

1．Intuitive Considerations151

2．Formal Development157

CHAPTER 9 STIELTJES INTEGRALS167

CHAPTER 10 THE FUNDAMENTAL THEOREM FOR CONTINUOUS GAMES183

1．The Value of a Continuous Game183

2．Two Algebraic Lemmas184

3．The Fundamental Theorem186

4．Devices for Computing and Verifying Solutions193

CHAPTER 11 SEPARABLE GAMES219

1．The Mapping Method219

2．An Illustrative Example230

3．Fixed-points237

4．Further Examples244

5．Rectangular Game Solved as a Separable Game251

6．Constrained Game Solved as a Separable Game254

CHAPTER 12 GAMES WITH CONVEX PAYOFF FUNCTIONS259

1．Convex Functions259

2．A Unique Strategy for One Player262

3．Strategies for the Other Player266

4．Remarks and an Example270

CHAPTER 13 APPLICATIONS TO STATISTICAL INFERENCE277

CHAPTER 14 LINEAR PROGRAMMING291

CHAPTER 15 ZERO-SUM n-PERSON GAMES303

1．Characteristic Functions303

2．Reduced Form313

CHAPTER 16 SOLUTIONS OF n-PERSON GAMES325

1．Imputations325

2．Definition of a Solution329

3．Isomorphic Games332

4．Three-person Games335

CHAPTER 17 GAMES WITHOUT ZERO-SUM RESTRICTION:THE VON NEUMANN-MORGENSTERN THEORY343

1．Characteristic Functions343

2．Imputations and Solutions348

CHAPTER 18 SOME OPEN PROBLEMS355

1．Two Types of Problems355

2．Games Played over Function Space355

3．Pseudo-games357

4．Non-zero-sum Games and n-Person Games358

BIBLIOGRAPHY361

INDEX369

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