Theory of Games and Economic Behavior: 60th Anniversary Commemorative Edition
Paperback
- Sale Price:
- $49.00/£40.60
- Price:
-
$70.00/£58.00 - ISBN:
- Published:
- Mar 19, 2007
- Copyright:
- 2004
- Illus:
- 105 line illus. 9 tables.
- Main_subject:
- Economics & Finance
30% off with code PUP30
ebook
- Sale Price:
- $49.00/£40.60
- Price:
-
$70.00/£58.00 - ISBN:
- Published:
- Mar 19, 2007
- Copyright:
- 2004
- Illus:
- 105 line illus. 9 tables.
- Main_subject:
- Economics & Finance
30% off with code PUP30
This is the classic work upon which modern-day 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 real-world 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.
John von Neumann (1903-1957) was one of the greatest mathematicians of the twentieth century and a pioneering figure in computer science. A native of Hungary who held professorships in Germany, he was appointed Professor of Mathematics at the Institute for Advanced Study (IAS) in 1933. Later he worked on the Manhattan Project, helped develop the IAS computer, and was a consultant to IBM. An important influence on many fields of mathematics, he is the author of Functional Operators, Mathematical Foundations of Quantum Mechanics, and Continuous Geometry (all Princeton). Oskar Morgenstern (1902-1977) taught at the University of Vienna and directed the Austrian Institute of Business Cycle Research before settling in the United States in 1938. There he joined the faculty of Princeton University, eventually becoming a professor and from 1948 directing its econometric research program. He advised the United States government on a wide variety of subjects. Though most famous for the book he co-authored with von Neumann, Morgenstern was also widely known for his skepticism about economic measurement, as reflected in one of his many other books, On the Accuracy of Economic Observations (Princeton). Harold Kuhn is Professor Emeritus of Mathematical Economics at Princeton University. Ariel Rubinstein is Professor of Economics at Tel Aviv University and at New York University.
- 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 set-theoretical 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 SET-THEORETICAL 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 zero-sum restriction
- CHAPTER III
- ZERO-SUM TWO-PERSON GAMES: THEORY
- 12. PRELIMINARY SURVEY
- 12.1. General viewpoints
- 12.2. The one-person 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
- ZERO-SUM TWO-PERSON 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
- ZERO-SUM THREE-PERSON 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: ZERO-SUM n-PERSON 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 ZERO-SUM THREE-PERSON 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 ZERO-SUM THREE-PERSON 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
- ZERO-SUM FOUR-PERSON 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, 3-symmetric four person game
- CHAPTER IX
- COMPOSITION AND DECOMPOSITION OF GAMES
- 41. COMPOSITION AND DECOMPOSITION
- 41.1. Search for n-person 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 non-isolated 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, |Γ|1. |Γ|2. 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 THREE-PERSON 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 NON-ZERO-SUM 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. Zero-sum and constant-sum 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 twentieth-century 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 self-respecting 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 all-time 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