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 v
TECHNICAL NOTE v
ACKNOWLEDGMENT x
CHAPTER I: FORMULATION OF THE ECONOMIC PROBLEM
1.THE MATHEMATICAL METHOD IN ECONOMICS 1
1.1. Introductory remarks 1
1.2. Difficulties of the application of the mathematical method 2
1.3. Necessary limitations of the objectives 6
1.4. Concluding remarks 7
2.QUALITATIVE DISCUSSION OF THE PROBLEM OF RATIONAL BEHAVIOR 8
2.1. The problem of rational behavior 8
2.2. "Robinson Crusoe" economy and social exchange economy 9
2.3. The number of variables and the number of participants 12
2.4. The case of many participants: Free competition 13
2.5. The "Lausanne" theory 15
3.THE NOTION OF UTILITY 15
3.1. Preferences and utilities 15
3.2. Principles of measurement: Preliminaries 16
3.3. Probability and numerical utilities 17
3.4. Principles of measurement: Detailed discussion 20
3.5. Conceptual structure of the axiomatic treatment of numerical utilities 24
3.6. The axioms and their interpretation 26
3.7. General remarks concerning the axioms 28
3.8. The role of the concept of marginal utility 29
4.STRUCTURE OF THE THEORY: SOLUTIONS AND STANDARDS OF BEHAVIOR 31
4.1. The simplest concept of a solution for one participant 31
4.2. Extension to all participants 33
4.3. The solution as a set of imputations 34
4.4. The intransitive notion of "superiority" or "domination" 37
4.5. The precise definition of a solution 39
4.6. Interpretation of our definition in terms of "standards of behavior" 40
4.7. Games and social organizations 43
4.8. Concluding remarks 43
CHAPTER II: GENERAL FORMAL DESCRIPTION OF GAMES OF STRATEGY
5.Introduction 46
5.1. Shift of emphasis from economics to games 46
5.2. General principles of classification and of procedure 46
6.THE SIMPLIFIED CONCEPT OF A GAME 48
6.1. Explanation of the termini technici 48
6.2. The elements of the game 49
6.3. Information and preliminary 51
6.4. Preliminarity, transitivity, and signaling 51
7.THE COMPLETE CONCEPT OF A GAME 55
7.1. Variability of the characteristics of each move 55
7.2. The general description 57
8.SETS AND PARTITIONS 60
8.1. Desirability of a set-theoretical description of a game 60
8.2. Sets, their properties, and their graphical representation 61
8.3. Partitions, their properties, and their graphical representation 63
8.4. Logistic interpretation of sets and partitions 66
*9. THE SET-THEORETICAL DESCRIPTION OF A CAME 67
*9.1. The partitions which describe a game 67
*9.2. Discussion of these partitions and their properties 71
*10. AXIOMATIC FORMULATION 73
*10.1. The axioms and their interpretations 73
*10.2. Logistic discussion of the axioms 76
*10.3. General remarks concerning the axioms 76
*10.4. Graphical representation 77
11.STRATEGIES AND THE FINAL SIMPLIFICATION OF THE DESCRIPTION OF THE GAME 79
11.1. The concept of a strategy and its formalization 79
11.2. The final simplification of the description of a game 81
11.3. The role of strategies in the simplified form of a game 84
11.4. The meaning of the zero-sum restriction 84
CHAPTER III: ZERO-SUM TWO-PERSON GAMES: THEORY
12.PRELIMINARY SURVEY 85
12.1. General viewpoints 85
12.2. The one-person game 85
12.3. Chance afid probability 87
12.4. The next objective 87
13.FUNCTIONAL CALCULUS 88
13.1. Basic definitions 88
13.2. The operations Max and Min 89
13.3. Commutativity questions 91
13.4. The mixed case. Saddle points 93
13.5. Proofs of the main facts 95
14.STRICTLY DETERMINED GAMES 98
141. Formulation of the problem 98
14.2. The minorant and the majorant games 100
14.3. Discussion of the auxiliary games 101
14.4. Conclusions 105
14.5. Analysis of strict determinateness 106
14.6. The interchange of players. Symmetry 109
14.7. Non strictly determined games 110
14.8. Program of a detailed analysis of strict determinateness 111
*15. GAMES WITH PERFECT INFORMATION
*15.1. Statement of purpose. Induction 112
*15.2. The exact condition (First step) 114
*15.3. The exact condition (Entire induction) 116
*15.4. Exact discussion of the inductive step 117
*15.5. Exact discussion of the inductive step (Continuation) 120
*15.6. The result in the case of perfect information 123
*15.7. Application to Chess 124
*15.8. The alternative, verbal discussion 126
16.LINEARITY AND CONVEXITY 128
16.1. Geometrical background 128
16.2. Vector operations 129
16.3. The theorem of the supporting hyperplanes 134
16.4. The theorem of the alternative for matrices 138
17.MIXED STRATEGIES. THE SOLUTION FOR ALL GAMES 143
17.1. Discussion of two elementary examples 143
17.2. Generalization of this viewpoint 145
17.3. Justification of the procedure as applied to an individual play 146
17.4. The minorant and the majorant games. (For mixed strategies) 149
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