CONTENTS

Preface

Technical Note

Acknowledgment


Chapter I. Formulation of the Economic Problem.

  1. The Mathematical Method in Economics.
	  1.1.
	  1.2.
	  1.3.
	  1.4.

  2. Qualitative Discussion of the Problem of Rational Behavior.
	  2.1.
	  2.2.
	  2.3.
	  2.4.
	  2.5.

  3. The Notion of Utility.
	  3.1.
	  3.2.
	  3.3.
	  3.4.
	  3.5.
	  3.6.
	  3.7.
	  3.8.

  4. Structure of the Theory: Solutions and Standards of Behavior.
	  4.1.
	  4.2.
	  4.3.
	  4.4.
	  4.5.
	  4.6.
	  4.7.
	  4.8.


Chapter II. General Formal Description of Games of Strategy.

  5. Introduction.
	  5.1.
	  5.2.

  6. The Simplified Concept of a Game.
	  6.1.
	  6.2.
	  6.3.
	  6.4.

  7. The Complete Concept of a Game.
	  7.1.
	  7.2.

  8. Sets and Partitions.
	  8.1.
	  8.2.
	  8.3.
	  8.4.

* 9. The Set-Theoretical Description of a Game.
	  9.1.
	  9.2.

*10. Axiomatic Formulation.
	*10.1.
	*10.2.
	*10.3.
	*10.4.

 11. Strategies and the Final Simplification of the Description of a Game.
	 11.1.
	 11.2.
	 11.3.
	 11.4.


Chapter III. Zero-Sum Two-Person Games: Theory.

 12. Preliminary Survey.
	 12.1.
	 12.2.
	 12.3.
	 12.4.

 13. Functional Calculus.
	 13.1.
	 13.2.
	 13.3.
	 13.4.
	 13.5.

 14. Strictly Determined.
	 14.1.
	 14.2.
	 14.3.
	 14.4.
	 14.5.
	 14.6.
	 14.7.
	 14.8.

*15. Games with Perfect Information.
	*15.1.
	*15.2.
	*15.3.
	*15.4.
	*15.5.
	*15.6.
	*15.7.
	*15.8.

 16. Linearity and Convexity.
	 16.1.
	 16.2.
	 16.3.
	 16.4.

 17. Mixed Strategies. The Solution for All Games.
	 17.1.
	 17.2.
	 17.3.
	 17.4.
	 17.5.
	 17.6.
	 17.7.
	 17.8.
	 17.9.
	 17.10.
	 17.11.


Chapter IV. Zero-Sum Two-Person Games: Examples.
 18. Some Elementary Games.
	 18.1.
	 18.2.
	 18.3.
	 18.4.
	 18.5.
	 18.6.
	 18.7.

*19. Poker and Bluffing.
	*19.1.
	*19.2.
	*19.3.
	*19.4.
	*19.5.
	*19.6.
	*19.7.
	*19.8.
	*19.9.
	*19.10.
	*19.11.
	*19.12.
	*19.13.
	*19.14.
	*19.15.
	*19.16.


Chapter V. Zero-um Three-Person Games.

 20. Preliminary Survey.
	20.1.
	20.2.

 21. The Simple Majority Game of Three Persons.
	21.1.
	21.2.
	21.3.

 22. Further Examples.
	22.1.
	22.2.
	22.3.

 23. The General Case.
	23.1.
	23.2.

 24. Discussion of an Objection.
	24.1.
	24.2.


Chapter VI. Formulation of the General Theory: Zero-Sum n-Person Games.

 25. The Characteristic Function.
	25.1.
	25.2.
	25.3.
	25.4.

 26. Construction of a Game with a Given Characteristic Function.
	26.1.
	26.2.

 27. Strategic Equivalence. Inessential and Essential Games.
	27.1.
	27.2.
	27.3.
	27.4.
	27.5.
	27.6.

 28. Groups, Simmetry and Fairness.
	28.1.
	28.2.

 29. reconsideration of the Zero-Sum Three-Person Game.
	29.1.
	29.2.

 30. The Exact Form of the General Definitions.
	30.1
	30.2
	*30.3
	30.4

 31. First Consequences.
	31.1.
	31.2.
	31.3.

 32. Determination of All Solutions of the Essential Zero-Sum Three-Person Game.
	32.1.
	32.2.

 33. Conclusions.
	33.1.
	33.2.


Chapter VII. Zero-Sum Four-Person Games.

 34. Preliminary Survey.
	34.1.
	34.2.
	34.3.

 35. Discussion of Some Special Points in the Cube Q.
	35.1.
	35.2.
	35.3.

 36. Discussion of the Main Diagonals.
	36.1.
	36.2.
	36.3.

 37. The Center and Its Environs.
	37.1.
	37.2.
	37.3.
	37.4.
	37.5.
	37.6.

*38. A Family of Solutions for a Neighborhood of the Center.
	*38.1.
	*38.2.
	*38.3.


Chapter VIII. Some Remarks Concerning n >= 5 Participants.

 39. The Number of Parameters in Various Classes of Games.
	39.1.
	39.2.

 40. The Symmetric Five Person Game.
	40.1.
	40.2.
	40.3.


Chapter IX. Composition and Decomposition of Games.

 41. Composition and Decomposition.
	41.1.
	41.2.
	41.3.
	41.4.
	41.5.

 42. Modification of the Theory.
	42.1.
	42.2.
	42.3.
	42.4.
	42.5.

 43. The Decomposition Partition.
	43.1.
	43.2.
	43.3.
	43.4.

 44. Decomposable Games. Further Extension of the Theory.
	44.1.
	44.2.
	44.3.
	44.4.
	44.5.
	44.6.
	44.7.

 45. Limitations of the Excess. Structure of the Extended Theory.
	45.1.
	45.2.
	45.3.
	45.4.
	45.5.
	45.6.

 46. Determination of All Solutions of a Decomposable Game.
	46.1.
	46.2.
	46.3.
	46.4.
	46.5.
	46.6.
	46.7.
	46.8.
	46.9.
	46.10.
	46.11.
	46.12.

 47. The Essential Three-Person Game in the New Theory
	47.1.
	47.2.
	47.3.
	47.4.
	47.5.
	47.6.
	47.7.
	47.8.
	47.9.


Chapter X. Simple Games.

 48. Winning and Losing Coalitions and Games Where They Occur
	48.1.
	48.2.

 49. Characterization of the Simple Games.
	49.1.
	49.2.
	49.3.
	49.4.
	49.5.
	49.6.
	49.7.

 50. The Majority Games and the Main Solution.
	50.1.
	50.2.
	50.3.
	50.4.
	50.5.
	50.6.
	50.7.
	50.8.

 51. Methods for the Enumeration of All Simple Games.
	51.1.
	51.2.
	51.3.
	51.4.
	51.5.
	51.6.
	51.7.

 52. The Simple Games for Small n.
	52.1.
	52.2.
	52.3.
	52.4.
	52.5.

 53. The New Possibilities of Simple Games for n >= 6.
	53.1.
	53.2.

 54. Determination of All Solutions in Suitable Games.
	54.1.
	54.2.
	54.3.

*55. The Simple Game [1, ..., 1, n - 2]
	*55.1
	*55.2
	*55.3
	*55.4
	*55.5
	*55.6
	*55.7
	*55.8
	*55.9
	*55.10
	*55.11
	*55.12


Chapter XI. General Non-Zero-Sum Games.

 56. Extension of the Theory.
	56.1.
	56.2.
	56.3.
	56.4.
	56.5.
	56.6.
	56.7.
	56.8.
	56.9.
	56.10.
	56.11.
	56.12.

 57. The Characteristic Function and Related Topics.
	57.1.
	57.2.
	57.3.
	57.4.
	57.5.

 58. Interpretation of the Characteristic Function.
	58.1.
	58.2.
	58.3.

 59. General COnsiderations.
	59.1.
	59.2.
	59.3.

 60. The Solutions of All general Games with n <= 3
	60.1.
	60.2.
	60.3.
	60.4.

 61. Economic Interpretation of the Results for n = 1, 2
	61.1.
	61.2.
	61.3.
	61.4.
	61.5.
	61.6.

 62. Economic Interpretation of the Results for n = 3: Special Case.
	62.1.
	62.2.
	62.3.
	62.4.
	62.5.
	62.6.

 63. Economic Interpretation of the Results for n = 3: General Case.
	63.1.
	63.2.
	63.3.
	63.4.
	63.5.
	63.6.

 64. The General Market.
	64.1.
	64.2.

Chapter XII. Extension of the Concepts of Domination and Solution.

 65. The Extension. Special Cases.
	65.1.
	65.2.
	65.3.
	65.4.
	65.5.
	65.6.
	65.7.
	65.8.
	65.9.

 66. Generalizazions of the Concept of Utility.
	66.1.
	66.2.
	66.3.
	66.4.

 67. Discussion of an Example.
	67.1.
	67.2.
	67.3.
	67.4.

Appendix: The Axiomatic Treatment of Utility.
Index of Figures.
Index of Names.
Index of Subjects.