Table of Contents
PREFACE v
TECHNICAL NOTE v
ACKNOWLEDGMENT x
CHAPTER I: FORMULATION OF THE ECONOMIC PROBLEM
1. THE MATHEMATICAL METHOD IN ECONOMICS 1
2. QUALITATIVE DISCUSSION OF THE PROBLEM OF RATIONAL BEHAVIOR 8
3. THE NOTION OF UTILITY 15
4. STRUCTURE OF THE THEORY: SOLUTIONS AND STANDARDS OF BEHAVIOR 31
CHAPTER II: GENERAL FORMAL DESCRIPTION OF GAMES OF STRATEGY
5. Introduction 46
6. THE SIMPLIFIED CONCEPT OF A GAME 48
7. THE COMPLETE CONCEPT OF A GAME 55
8. SETS AND PARTITIONS 60
*9. THE SET-THEORETICAL DESCRIPTION OF A CAME 67
*10. AXIOMATIC FORMULATION 73
11. STRATEGIES AND THE FINAL SIMPLIFICATION OF THE DESCRIPTION OF THE GAME 79
CHAPTER III: ZERO-SUM TWO-PERSON GAMES: THEORY
12. PRELIMINARY SURVEY 85
13. FUNCTIONAL CALCULUS 88
14. STRICTLY DETERMINED GAMES 98
*15. GAMES WITH PERFECT INFORMATION
16. LINEARITY AND CONVEXITY 128
17. MIXED STRATEGIES. THE SOLUTION FOR ALL GAMES 143
CHAPTER IV: ZERO-SUM TWO-PERSON GAMES: EXAMPLES
18. SOME ELEMENTARY GAMES 169
*19. POKER AND BLUFFING 186
CHAPTER V: ZERO-SUM THREE-PERSON GAMES
20. PRELIMINARY SURVEY 220
21. THE SIMPLE MAJORITY GAME OF THREE PERSONS 222
22. FURTHER EXAMPLES 225
23. THE GENERAL CASE 231
24. DISCUSSION OF AN OBJECTION 233
CHAPTER VI: FORMULATION OF THE GENERAL THEORY: ZERO-SUM n-PERSON GAMES
25. THE CHARACTERISTIC FUNCTION 238
26. CONSTRUCTION OF A GAME WITH A GIVEN CHARACTERISTIC FUNCTION 243
27. STRATEGIC EQUIVALENCE. INESSENTIAL AND ESSENTIAL GAMES 245
28. GROUPS, SYMMETRY AND FAIRNESS 255
29. RECONSIDERATION OF THE ZERO-SUM THREE-PERSON GAME 260
30. THE EXACT FORM OF THE GENERAL DEFINITIONS 263
31. FIRST CONSEQUENCES 272
32. DETERMINATION OF ALL SOLUTIONS OF THE ESSENTIAL ZERO-SUM THREE-PERSON GAME 282
33. CONCLUSIONS 288
CHAPTER VII: ZERO-SUM FOUR-PERSON GAMES
34. PRELIMINARY SURVEY 291
35. DISCUSSION OF SOME SPECIAL POINTS IN THE CUBE Q 295
36. DISCUSSION OF THE MAIN DIAGONALS 304
37. THE CENTER AND ITS ENVIRONS 313
*38. A FAMILY OF SOLUTIONS FOR A NEIGHBORHOOD OF THE CENTER 321
CHAPTER VIII: SOME REMARKS CONCERNING n [equal to or greater than] 5 PARTICIPANTS
39. THE NUMBER OF PARAMETERS IN VARIOUS CLASSES OF GAMES 330
40. THE SYMMETRIC FIVE PERSON GAME 332
CHAPTER IX: COMPOSITION AND DECOMPOSITION OF GAMES
41. COMPOSITION AND DECOMPOSITION 339
42. MODIFICATION OF THE THEORY 345
43. THE DECOMPOSITION PARTITION 353
44. DECOMPOSABLE GAMES. FURTHER EXTENSION OF THE THEORY 358
45. LIMITATIONS OF THE EXCESS. STRUCTURE OF THE EXTENDED THEORY 378
46. DETERMINATION OF ALL SOLUTIONS OF A DECOMPOSABLE GAME 381
47. THE ESSENTIAL THREE-PERSON GAME IN THE NEW THEORY 403
CHAPTER X: SIMPLE GAMES
48. WINNING AND LOSING COALITIONS AND GAMES WHERE THEY OCCUR 420
49. CHARACTERIZATION OF THE SIMPLE GAMES 423
50. THE MAJORITY GAMES AND THE MAIN SOLUTION 431
51. METHODS FOR THE ENUMERATION OF ALL SIMPLE GAMES 445
52. THE SIMPLE GAMES FOR SMALL n 457
53. THE NEW POSSIBILITIES OF SIMPLE GAMES FOR n [equal to or greater than] 6 463
54. DETERMINATION OF ALL SOLUTIONS IN SUITABLE GAMES 470
*55. THE SIMPLE GAME [1, . . . , 1, n - 2]h 473
CHAPTER XI: GENERAL NON-ZERO-SUM GAMES
56. EXTENSION OF THE THEORY 504
57. THE CHARACTERISTIC FUNCTION AND RELATED TOPICS 527
58. INTERPRETATION OF THE CHARACTERISTIC FUNCTION 538
59. GENERAL CONSIDERATIONS 542
60. THE SOLUTIONS OF ALL GENERAL GAMES WITH n [equal to or less than] 3 548
61. ECONOMIC INTERPRETATION OF THE RESULTS FOR n = 1, 2 555
62. ECONOMIC INTERPRETATION OF THE RESULTS FOR n = 3: SPECIAL CASE 564
63. ECONOMIC INTERPRETATION OF THE RESULTS FOR n = 3: GENERAL CASE 573
64. THE GENERAL MARKET 583
CHAPTER XII: EXTENSION OF THE CONCEPTS OF DOMINATION AND SOLUTION
65. THE EXTENSION. SPECIAL CASES 587
66. GENERALIZATION OF THE CONCEPT OF UTILITY 603
67. DISCUSSION OF AN EXAMPLE 608
APPENDIX: THE AXIOMATIC TREATMENT OF UTILITY 617
INDEX OF FIGURES 633
INDEX OF NAMES 634
INDEX OF SUBJECTS 635
