Theory of Games and Economic Behavior: 60th Anniversary Commemorative Edition

Introduction by
 Harold William Kuhn

Afterword by
 Ariel Rubinstein
Paperback
 Price:
 $70.00 / £54.00
 ISBN:
 Published:
 Apr 8, 2007
 Copyright:
 2004
 Pages:
 776
 Size:
 6 x 9.25 in.
 Illus:
 105 line illus. 9 tables.
ebook
 Price:
 $70.00 / £54.00
 ISBN:
 Published:
 Apr 8, 2007
 Copyright:
 2004
 Pages:
 776
 Size:
 6 x 9.25 in.
 Illus:
 105 line illus. 9 tables.
This is the classic work upon which modernday game theory is based. What began more than sixty years ago as a modest proposal that a mathematician and an economist write a short paper together blossomed, in 1944, when Princeton University Press published Theory of Games and Economic Behavior. In it, John von Neumann and Oskar Morgenstern conceived a groundbreaking mathematical theory of economic and social organization, based on a theory of games of strategy. Not only would this revolutionize economics, but the entirely new field of scientific inquiry it yielded — game theory — has since been widely used to analyze a host of realworld phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations. And it is today established throughout both the social sciences and a wide range of other sciences.
This sixtieth anniversary edition includes not only the original text but also an introduction by Harold Kuhn, an afterword by Ariel Rubinstein, and reviews and articles on the book that appeared at the time of its original publication in the New York Times, tthe American Economic Review, and a variety of other publications. Together, these writings provide readers a matchless opportunity to more fully appreciate a work whose influence will yet resound for generations to come.
 PREFACE
 TECHNICAL NOTE
 ACKNOWLEDGMENT
 CHAPTER I
 FORMULATION OF THE ECONOMIC PROBLEM
 1. THE MATHEMATICAL METHOD IN ECONOMICS
 1.1. Introductory remarks
 1.2. Difficulties of the application of the mathematical method
 1.3. Necessary limitations of the objectives
 1.4. Concluding remarks
 2. QUALITATIVE DISCUSSION OF THE PROBLEM OF RATIONAL BEHAVIOR
 2.1. The problem of rational behavior
 2.2. “Robinson Crusoe” economy and social exchange economy
 2.3. The number of variables and the number of participants
 2.4. The case of many participants: Free competition
 2.5. The “Lausanne” theory
 3. THE NOTION OF UTILITY
 3.1. Preferences and utilities
 3.2. Principles of measurement: Preliminaries
 3.3. Probability and numerical utilities
 3.4. Principles of measurement: Detailed discussion
 3.5. Conceptual structure of the axiomatic treatment of numerical utilities
 3.6. The axioms and their interpretation
 3.7. General remarks concerning the axioms
 3.8. The role of the concept of marginal utility
 4. STRUCTURE OF THE THEORY: SOLUTIONS AND STANDARDS OF BEHAVIOR
 4.1. The simplest concept of a solution for one participant
 4.2. Extension to all participants
 4.3. The solution as a set of imputations
 4.4. The intransitive notion of “superiority” or “domination”
 4.5. The precise definition of a solution
 4.6. Interpretation of our definition in terms of “standards of behavior”
 4.7. Games and social organizations
 4.8. Concluding remarks
 CHAPTER II
 GENERAL FORMAL DESCRIPTION OF GAMES OF STRATEGY
 5. INTRODUCTION
 5.1. Shift of emphasis from economics to games
 5.2. General principles of classification and of procedure
 6. THE SIMPLIFIED CONCEPT OF A GAME
 6.1. Explanation of the termini technici
 6.2. The elements of the game
 6.3. Information and preliminary
 6.4. Preliminarity, transitivity, and signaling
 7. THE COMPLETE CONCEPT OF A GAME
 7.1. Variability of the characteristics of each move
 7.2. The general description
 8. SETS AND PARTITIONS
 8.1. Desirability of a settheoretical description of a game
 8.2. Sets, their properties, and their graphical representation
 8.3. Partitions, their properties, and their graphical representation
 8.4. Logistic interpretation of sets and partitions
 *9. THE SETTHEORETICAL DESCRIPTION OF A GAME
 *9.1. The partitions which describe a game
 *9.2. Discussion of these partitions and their properties
 *10. AXIOMATIC FORMULATION
 *10.1. The axioms and their interpretations
 *10.2. Logistic discussion of the axioms
 *10.3. General remarks concerning the axioms
 *10.4. Graphical representation
 11. STRATEGIES AND THE FINAL SIMPLIFICATION OF THE DESCRIPTION OF A GAME
 11.1. The concept of a strategy and its formalization
 11.2. The final simplification of the description of a game
 11.3. The role of strategies in the simplified form of a game
 11.4. The meaning of the zerosum restriction
 CHAPTER III
 ZEROSUM TWOPERSON GAMES: THEORY
 12. PRELIMINARY SURVEY
 12.1. General viewpoints
 12.2. The oneperson game
 12.3. Chance and probability
 12.4. The next objective
 13. FUNCTIONAL CALCULUS
 13.1. Basic definitions
 13.2. The operations Max and Min
 13.3 Commutativity questions
 13.4. The mixed case. Saddle points
 13.5. Proofs of the main facts
 14. STRICTLY DETERMINED GAMES
 14 1. Formulation of the problem
 14.2. The minorant and the majorant games
 14.3. Discussion of the auxiliary games
 14.4. Conclusions
 14.5. Analysis of strict determinateness
 14.6. The interchange of players. Symmetry
 14.7. Non strictly determined games
 14.8. Program of a detailed analysis of strict determinateness
 *15. GAMES WITH PERFECT INFORMATION
 *15.1. Statement of purpose. Induction
 *15.2. The exact condition (First step)
 *15.3. The exact condition (Entire induction)
 *15.4. Exact discussion of the inductive step
 *15.5. Exact discussion of the inductive step (Continuation)
 *15.6. The result in the case of perfect information
 *15.7. Application to Chess
 *15.8. The alternative, verbal discussion
 16. LINEARITY AND CONVEXITY
 16.1. Geometrical background
 16.2. Vector operations
 16.3. The theorem of the supporting hyperplanes
 16.4. The theorem of the alternative for matrices
 17. MIXED STRATEGIES. THE SOLUTION FOR ALL GAMES
 17.1. Discussion of two elementary examples
 17.2. Generalization of this viewpoint
 17.3. Justification of the procedure as applied to an individual play
 17.4. The minorant and the majorant games. (For mixed strategies)
 17.5. General strict determinateness
 17.6. Proof of the main theorem
 17.7. Comparison of the treatment by pure and by mixed strategies
 17.8. Analysis of general strict determinateness
 17.9. Further characteristics of good strategies
 17.10. Mistakes and their consequences. Permanent optimality
 17.11. The interchange of players. Symmetry
 CHAPTER IV
 ZEROSUM TWOPERSON GAMES: EXAMPLES
 18. SOME ELEMENTARY GAMES
 18.1. The simplest games
 18.2. Detailed quantitative discussion of these games
 18.3. Qualitative characterizations
 18.4. Discussion of some specific games. (Generalized forms of Matching Pennies)
 18.5. Discussion of some slightly more complicated games
 18.6. Chance and imperfect information
 18.7. Interpretation of this result
 *19. POKER AND BLUFFING
 *19.1. Description of Poker
 *19.2. Bluffing
 *19.3. Description of Poker (Continued)
 *19.4. Exact formulation of the rules
 *19.5. Description of the strategy
 *19.6. Statement of the problem
 *19.7. Passage from the discrete to the continuous problem
 *19.8. Mathematical determination of the solution
 *19.9. Detailed analysis of the solution
 *19.10. Interpretation of the solution
 *19.11. More general forms of Poker
 *19.12. Discrete hands
 *19.13. m possible bids
 *19.14. Alternate bidding
 *19.15. Mathematical description of all solutions
 *19.16. Interpretation of the solutions. Conclusions
 CHAPTER V
 ZEROSUM THREEPERSON GAMES
 20. PRELIMINARY SURVEY
 20.1. General viewpoints
 20.2. Coalitions
 21. THE SIMPLE MAJORITY GAME OF THREE PERSONS
 21.1. Definition of the game
 21.2. Analysis of the game: Necessity of “understandings”
 21.3. Analysis of the game: Coalitions. The role of symmetry
 22. FURTHER EXAMPLES
 22.1. Unsymmetric distributions. Necessity of compensations
 22.2. Coalitions of different strength. Discussion
 22.3. An inequality. Formulae
 23. THE GENERAL CASE
 23.1. Detailed discussion. Inessential and essential games
 23.2. Complete formulae
 24. DISCUSSION OF AN OBJECTION
 24.1. The case of perfect information and its significance
 24.2. Detailed discussion. Necessity of compensations between three or more players
 CHAPTER VI
 FORMULATION OF THE GENERAL THEORY: ZEROSUM nPERSON GAMES
 25. THE CHARACTERISTIC FUNCTION
 25.1. Motivation and definition
 25.2. Discussion of the concept
 25.3. Fundamental properties
 25.4. Immediate mathematical consequences
 26. CONSTRUCTION OF A GAME WITH A GIVEN CHARACTERISTIC FUNCTION
 26.1. The construction
 26.2. Summary
 27. STRATEGIC EQUIVALENCE. INESSENTIAL AND ESSENTIAL GAMES
 27.1. Strategic equivalence. The reduced form
 27.2. Inequalities. The quantity γ
 27.3. Inessentiality and essentiality
 27.4. Various criteria. Non additive utilities
 27.5. The inequalities in the essential case
 27.6. Vector operations on characteristic functions
 28. GROUPS, SYMMETRY AND FAIRNESS
 28.1. Permutations, their groups and their effect on a game
 28.2. Symmetry and fairness
 29. RECONSIDERATION OF THE ZEROSUM THREEPERSON GAME
 29.1. Qualitative discussion
 29.2. Quantitative discussion
 30. THE EXACT FORM OF THE GENERAL DEFINITIONS
 30.1. The definitions
 30.2. Discussion and recapitulation
 *30.3. The concept of saturation
 30.4. Three immediate objectives
 31. FIRST CONSEQUENCES
 31.1. Convexity, flatness, and some criteria for domination
 31.2. The system of all imputations. One element solutions
 31.3. The isomorphism which corresponds to strategic equivalence
 32. DETERMINATION OF ALL SOLUTIONS OF THE ESSENTIAL ZEROSUM THREEPERSON GAME
 32.1. Formulation of the mathematical problem. The graphical method
 32.2. Determination of all solutions
 33. CONCLUSIONS
 33.1. The multiplicity of solutions. Discrimination and its meaning
 33.2. Statics and dynamics
 CHAPTER VII
 ZEROSUM FOURPERSON GAMES
 34. PRELIMINARY SURVEY
 34.1. General viewpoints
 34.2. Formalism of the essential zero sum four person games
 34.3. Permutations of the players
 35. DISCUSSION OF SOME SPECIAL POINTS IN THE CUBE Q
 35.1. The corner I. (and V., VI., VII.)
 35.2. The corner VIII. (and II., III., IV.,). The three person game and a “Dummy”
 35.3. Some remarks concerning the interior of Q
 36. DISCUSSION OF THE MAIN DIAGONALS
 36.1. The part adjacent to the corner VIII.: Heuristic discussion
 36.2. The part adjacent to the corner VIII.: Exact discussion
 *36.3. Other parts of the main diagonals
 37. THE CENTER AND ITS ENVIRONS
 37.1. First orientation about the conditions around the center
 37.2. The two alternatives and the role of symmetry
 37.3. The first alternative at the center
 37.4. The second alternative at the center
 37.5. Comparison of the two central solutions
 37.6. Unsymmetrical central solutions
 *38. A FAMILY OF SOLUTIONS FOR A NEIGHBORHOOD OF THE CENTER
 *38.1. Transformation of the solution belonging to the first alternative at the center
 *38.2. Exact discussion
 *38.3. Interpretation of the solutions
 CHAPTER VIII
 SOME REMARKS CONCERNING n ≥ 5 PARTICIPANTS
 39. THE NUMBER OF PARAMETERS IN VARIOUS CLASSES OF GAMES
 39.1. The situation for n = 3, 4
 39.2. The situation for all n ≥ 3
 40. THE SYMMETRIC FIVE PERSON GAME
 40.1. Formalism of the symmetric five person game
 40.2. The two extreme cases
 40.3. Connection between the symmetric five person game and the 1, 2, 3symmetric four person game
 CHAPTER IX
 COMPOSITION AND DECOMPOSITION OF GAMES
 41. COMPOSITION AND DECOMPOSITION
 41.1. Search for nperson games for which all solutions can be determined
 41.2. The first type. Composition and decomposition
 41.3. Exact definitions
 41.4. Analysis of decomposability
 41.5. Desirability of a modification
 42. MODIFICATION OF THE THEORY
 42.1. No complete abandonment of the zero sum restriction
 42.2. Strategic equivalence. Constant sum games
 42.3. The characteristic function in the new theory
 42.4. Imputations, domination, solutions in the new theory
 42.5. Essentiality, inessentiality and decomposability in the new theory
 43. THE DECOMPOSITION PARTITION
 43.1. Splitting sets. Constituents
 43.2. Properties of the system of all splitting sets
 43.3. Characterization of the system of all splitting sets. The decomposition partition
 43.4. Properties of the decomposition partition
 44. DECOMPOSABLE GAMES. FURTHER EXTENSION OF THE THEORY
 44.1. Solutions of a (decomposable) game and solutions of its constituents
 44.2. Composition and decomposition of imputations and of sets of imputations
 44.3. Composition and decomposition of solutions. The main possibilities and surmises
 44.4. Extension of the theory. Outside sources
 44.5. The excess
 44.6. Limitations of the excess. The nonisolated character of a game in the new setup
 44.7. Discussion of the new setup. E(e0), F(e0)
 45. LIMITATIONS OF THE EXCESS. STRUCTURE OF THE EXTENDED THEORY
 45.1. The lower limit of the excess
 45.2. The upper limit of the excess. Detached and fully detached imputations
 45.3. Discussion of the two limits, Γ1. Γ2. Their ratio
 45.4. Detached imputations and various solutions. The theorem connecting E(e0), F(e0)
 45.5. Proof of the theorem
 45.6. Summary and conclusions
 46. DETERMINATION OF ALL SOLUTIONS OF A DECOMPOSABLE GAME
 46.1. Elementary properties of decompositions
 46.2. Decomposition and its relation to the solutions: First results concerning F(e0)
 46.3. Continuation
 46.4. Continuation
 46.5. The complete result in F(e0)
 46.6. The complete result in E(e0)
 46.7. Graphical representation of a part of the result
 46.8. Interpretation: The normal zone. Heredity of various properties
 46.9. Dummies
 46.10. Imbedding of a game
 46.11. Significance of the normal zone
 46.12. First occurrence of the phenomenon of transfer: n = 6
 47. THE ESSENTIAL THREEPERSON GAME IN THE NEW THEORY
 47.1. Need for this discussion
 47.2. Preparatory considerations
 47.3. The six cases of the discussion. Cases (I)−(III)
 47.4. Case (IV): First part
 47.5. Case (IV): Second part
 47.6. Case (V)
 47.7. Case (VI)
 47.8. Interpretation of the result: The curves (one dimensional parts) in the solution
 47.9. Continuation: The areas (two dimensional parts) in the solution
 CHAPTER X
 SIMPLE GAMES
 48. WINNING AND LOSING COALITIONS AND GAMES WHERE THEY OCCUR
 48.1. The second type of 41.1. Decision by coalitions
 48.2. Winning and Losing Coalitions
 49. CHARACTERIZATION OF THE SIMPLE GAMES
 49.1. General concepts of winning and losing coalitions
 49.2. The special role of one element sets
 49.3. Characterization of the systems W, L of actual games
 49.4. Exact definition of simplicity
 49.5. Some elementary properties of simplicity
 49.6. Simple games and their W, L. The Minimal winning coalitions: Wm
 49.7. The solutions of simple games
 50. THE MAJORITY GAMES AND THE MAIN SOLUTION
 50.1. Examples of simple games: The majority games
 50.2. Homogeneity
 50.3. A more direct use of the concept of imputation in forming solutions
 50.4. Discussion of this direct approach
 50.5. Connections with the general theory. Exact formulation
 50.6. Reformulation of the result
 50.7. Interpretation of the result
 50.8. Connection with the Homogeneous Majority game.
 51. METHODS FOR THE ENUMERATION OF ALL SIMPLE GAMES
 51.1. Preliminary Remarks
 51.2. The saturation method: Enumeration by means of W
 51.3. Reasons for passing from W to Wm. Difficulties of using Wm
 51.4. Changed Approach: Enumeration by means of Wm
 51.5. Simplicity and decomposition
 51.6. Inessentiality, Simplicity and Composition. Treatment of the excess
 51.7. A criterium of decomposability in terms of Wm
 52. THE SIMPLE GAMES FOR SMALL n
 52.1. Program. n = 1, 2 play no role. Disposal of n = 3
 52.2. Procedure for n ≥ 4: The two element sets and their role in classifying the Wm
 52.3. Decomposability of cases C*, Cn−2, Cn−1
 52.4. The simple games other than [1, • • •, 1, n − 2]h (with dummies): The Cases Ck, k = 0, 1, • • •, n − 3
 52.5. Disposal of n = 4, 5
 53. THE NEW POSSIBILITIES OF SIMPLE GAMES FOR n ≥ 6
 53.1. The Regularities observed for n ≥ 6
 53.2. The six main counter examples (for n = 6, 7)
 54. DETERMINATION OF ALL SOLUTIONS IN SUITABLE GAMES
 54.1. Reasons to consider other solutions than the main solution in simple games
 54.2. Enumeration of those games for which all solutions are known
 54.3. Reasons to consider the simple game [1, • • •, 1, n – 2]h
 *55. THE SIMPLE GAME [1, • • •, 1, n – 2]h
 *55.1. Preliminary Remarks
 *55.2. Domination. The chief player. Cases (I) and (II)
 *55.3. Disposal of Case (I)
 *55.4. Case (II): Determination of Ṿ
 *55.5. Case (II): Determination of Ṿ
 *55.6. Case (II): a and S*
 *55.7. Case (II′) and (II″). Disposal of Case (II′)
 *55.8. Case (II″): a and V′. Domination
 *55.9. Case (II″): Determination of V′
 *55.10. Disposal of Case (II″)
 *55.11. Reformulation of the complete result
 *55.12. Interpretation of the result
 CHAPTER XI
 GENERAL NONZEROSUM GAMES
 56. EXTENSION OF THE THEORY
 56.1. Formulation of the problem
 56.2. The fictitious player. The zero sum extension Γ
 56.3. Questions concerning the character of Γ
 56.4. Limitations of the use of Γ
 56.5. The two possible procedures
 56.6. The discriminatory solutions
 56.7. Alternative possibilities
 56.8. The new setup
 56.9. Reconsideration of the case when Γ is a zero sum game
 56.10. Analysis of the concept of domination
 56.11. Rigorous discussion
 56.12. The new definition of a solution
 57. THE CHARACTERISTIC FUNCTION AND RELATED TOPICS
 57.1. The characteristic function: The extended and the restricted form
 57.2. Fundamental properties
 57.3. Determination of all characteristic functions
 57.4. Removable sets of players
 57.5. Strategic equivalence. Zerosum and constantsum games
 58. INTERPRETATION OF THE CHARACTERISTIC FUNCTION
 58.1. Analysis of the definition
 58.2. The desire to make a gain vs. that to inflict a loss
 58.3. Discussion
 59. GENERAL CONSIDERATIONS
 59.1. Discussion of the program
 59.2. The reduced forms. The inequalities
 59.3. Various topics
 60. THE SOLUTIONS OF ALL GENERAL GAMES WITH n ≦ 3
 60.1. The case n = 1
 60.2. The case n = 2
 60.3. The case n = 3
 60.4. Comparison with the zero sum games
 61. ECONOMIC INTERPRETATION OF THE RESULTS FOR n = 1, 2
 61.1. The case n = 1
 61.2. The case n = 2. The two person market
 61.3. Discussion of the two person market and its characteristic function
 61.4. Justification of the standpoint of 58
 61.5. Divisible goods. The “marginal pairs”
 61.6. The price. Discussion
 62. ECONOMIC INTERPRETATION OF THE RESULTS FOR n = 3: SPECIAL CASE
 62.1. The case n = 3, special case. The three person market
 62.2. Preliminary discussion
 62.3. The solutions: First subcase
 62.4. The solutions: General form
 62.5. Algebraical form of the result
 62.6. Discussion
 63. ECONOMIC INTERPRETATION OF THE RESULTS FOR n = 3: GENERAL CASE
 63.1. Divisible goods
 63.2. Analysis of the inequalities
 63.3. Preliminary discussion
 63.4. The solutions
 63.5. Algebraical form of the result
 63.6. Discussion
 64. THE GENERAL MARKET
 64.1. Formulation of the problem
 64.2. Some special properties. Monopoly and monopsony
 CHAPTER XII
 EXTENSION OF THE CONCEPTS OF DOMINATION AND SOLUTION
 65. THE EXTENSION. SPECIAL CASES
 65.1. Formulation of the problem
 65.2. General remarks
 65.3. Orderings, transitivity, acyclicity
 65.4. The solutions: For a symmetric relation. For a complete ordering
 65.5. The solutions: For a partial ordering
 65.6. Acyclicity and strict acyclicity
 65.7. The solutions: For an acyclic relation
 65.8. Uniqueness of solutions, acyclicity and strict acyclicity
 65.9. Application to games: Discreteness and continuity
 66. GENERALIZATION OF THE CONCEPT OF UTILITY
 66.1. The generalization. The two phases of the theoretical treatment
 66.2. Discussion of the first phase
 66.3. Discussion of the second phase
 66.4. Desirability of unifying the two phases
 67. DISCUSSION OF AN EXAMPLE
 67.1. Description of the example
 67.2. The solution and its interpretation
 67.3. Generalization: Different discrete utility scales
 67.4. Conclusions concerning bargaining
 APPENDIX: THE AXIOMATIC TREATMENT OF UTILITY
"Praise for Princeton's previous edition: "A rich and multifaceted work. . . . [S]ixty years later, the Theory of Games may indeed be viewed as one of the landmarks of twentiethcentury social science.""—Robert J. Leonard, History of Political Economics
"Praise for Princeton's previous edition: "Opinions still vary on the success of the project to put economics on a sound mathematical footing, but game theory was eventually hugely influential, especially on mathematics and the study of automata. Every selfrespecting library must have one.""—Mike Holderness, New Scientist
"While the jury is still out on the success or failure of game theory as an attempted palace coup within the economics community, few would deny that interest in the subject—as measured in numbers of journal page—is at or near an alltime high. For that reason alone, this handsome new edition of von Neumann and Morgenstern's still controversial classic should be welcomed by the entire research community."—James Case, SIAM News
"The main achievement of the book lies, more than in its concrete results, in its having introduced into economics the tools of modern logic and in using them with an astounding power of generalization."—The Journal of Political Economy
"One cannot but admire the audacity of vision, the perseverance in details, and the depth of thought displayed in almost every page of the book. . . . The appearance of a book of [this] calibre . . . is indeed a rare event."—The American Economic Review
"Posterity may regard this book as one of the major scientific achievements of the first half of the twentieth century. This will undoubtedly be the case if the authors have succeeded in establishing a new exact science—the science of economics. The foundation which they have laid is extremely promising."—The Bulletin of the American Mathematical Society