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Theory of Games and Economic Behavior (60th Anniversary Commemorative Edition)

Theory of Games and Economic Behavior (60th Anniversary Commemorative Edition)

John von Neumann
Oskar Morgenstern
With an introduction by Harold W. Kuhn
and an afterword by Ariel Rubinstein
Copyright Date: 1944
Pages: 776
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  • Book Info
    Theory of Games and Economic Behavior (60th Anniversary Commemorative Edition)
    Book Description:

    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 publishedTheory 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 theNew York Times, ttheAmerican 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.

    eISBN: 978-1-4008-2946-0
    Subjects: Economics, Mathematics

Table of Contents

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  1. Front Matter
    (pp. i-iv)
  2. Table of Contents
    (pp. v-vi)
  3. Introduction
    (pp. vii-xiv)

    Although John von Neumann was without doubt “the father of game theory,” the birth took place after a number of miscarriages. From an isolated and amazing minimax solution of a zero-sum two-person game in 1713 [1] to sporadic considerations by E. Zermelo [2], E. Borel [3], and H. Steinhaus [4], nothing matches the path-breaking paper of von Neumann, published in 1928 [5].

    This paper, elegant though it is, might have remained a footnote to the history of mathematics Were it not for collaboration of von Neumann with Oskar Morgenstern in the early ‘40s. Their joint efforts led to the publication...

  4. Theory of Games and Economic Behavior

    • Preface
      (pp. xxvii-xxx)
      John von Neumann and Oskar Morgenstern
      (pp. xxxi-xxxii)
      (pp. xxxii-xxxii)
      (pp. 1-45)

      1.1.1. The purpose of this book is to present a discussion of some fundamental questions of economic theory which require a treatment different from that which they have found thus far in the literature. The analysis is concerned with some basic problems arising from a study of economic behavior which have been the center of attention of economists for a long time. They have their origin in the attempts to find an exact description of the endeavor of the individual to obtain a maximum of utility, or, in the case of the entrepreneur, a maximum of profit. It is well...

      (pp. 46-84)

      5.1. It should be clear from the discussions of Chapter I that a theory of rational behavior—i.e. of the foundations of economics and of the main mechanisms of social organization—requires a thorough study of the “games of strategy.” Consequently we must now take up the theory of games as an independent subject. In studying it as a problem in its own right, our point of view must of necessity undergo a serious shift. In Chapter I our primary interest lay in economics. It was only after having convinced ourselves of the impossibility of making progress in that field...

      (pp. 85-168)

      12.1.1. In the preceding chapter we obtained an all-inclusive formal characterization of the general game ofnpersons (cf. 10.1.). We followed up by developing an exact concept of strategy which permitted us to replace the rather complicated general scheme of a game by a much more simple special one, which was nevertheless shown to be fully equivalent to the former (cf. 11.2.). In the discussion which follows it will sometimes be more convenient to use one form, sometimes the other. It is therefore desirable to give them specific technical names. We will accordingly call them theextensiveand the...

      (pp. 169-219)

      18.1.1. We have concluded our general discussion of the zero-sum two-person game. We shall now proceed to examine specific examples of such games. These examples will exhibit better than any general abstract discussions could, the true significance of the various components of our theory. They will show, in particular, how some formal steps which are dictated by our theory permit a direct common-sense interpretation. It will appear that we have here a rigorous formalization of the main aspects of such “practical” and “psychological” phenomena as those to be mentioned in 19.2., 19.10. and 19.16.¹

      18.1.2. The size of the numbers...

      (pp. 220-237)

      20.1.1. The theory of the zero-sum two-person game having been completed, we take the next step in the sense of 12.4.: We shall establish the theory of the zero-sum three-person game. This will bring entirely new viewpoints into play. The types of games discussed thus far have had also their own characteristic problems. We saw that the zero-sum one-person game was characterized by the emergence of a maximum problem and the zero-sum two-person game by the clear cut opposition of interest which could no longer be described as a maximum problem. And just as the transition from the one-person to...

      (pp. 238-290)

      25.1.1. We now turn to the zero-sumn-person game for generaln. The experience gained in Chapter V concerning the casen= 3 suggests that the possibilities of coalitions between players will play a decisive role in the general theory which we are developing. It is therefore important to evolve a mathematical tool which expresses these “possibilities” in a quantitative way.

      Since we have an exact concept of “value” (of a play) for the zero-sum two-person game, we can also attribute a “value” to any given group of players, provided that it is opposed by the coalition of all...

      (pp. 291-329)

      34.1. We are now in possession of a general theory of the zero-sumn-person game, but the state of our information is still far from satisfactory. Save for the formal statement of the definitions we have penetrated but little below the surface. The applications which we have made—i.e. the special cases in which we have succeeded in determining our solutions—can be rated only as providing a preliminary orientation. As pointed out in 30.4.2., these applications cover all casesn≦ 3, but we know from our past discussions how little this is in comparison with the general problem....

      (pp. 330-338)

      39.1. We know that the essential games constitute our real problem and that they may always be assumed in the reduced form and withγ= 1. In this representation there exists precisely one zero-sum three-person game, while the zero-sum four-person games form a three-dimensional manifold.¹ We have seen further that the (unique) zero-sum three-person game is automatically symmetric, while the three-dimensional manifold of all zero-sum four-person games contains precisely one symmetric game.

      Let us express this by stating, for each one of the above varieties of games, how many dimensions it possesses,—i.e. how many indefinite parameters must be...

      (pp. 339-419)

      41.1.1. The last two chapters will have conveyed a specific idea of the rapidity with which the complexity of our problem increases as the numbernof participants goes to 4,5, . . . etc. In spite of their incompleteness, those considerations tended to be so voluminous that it must seem completely hopeless to push this—casuistic—approach beyond five participants.¹ Besides, the fragmentary character of the results gained in this manner very seriously limits their usefulness in informing us about the general possibilities of the theory.

      On the other hand, it is absolutely vital to get some insight into...

      (pp. 420-503)

      48.1.1. The program formulated in 34.1. provided for far-reaching generalizations of the games corresponding to the 8 corners of the cubeQ, introduced in 34.2.2. The cornerVIII(also representative ofII, III, IV) was taken up in 35.2.1. and provided the source for a generalization, leading to the theory of composition and decomposition to which all of Chapter IX was devoted. We now pass to the cornerI(also representative ofV, VI, VII), which we will treat in a similar fashion.

      By generalizing the principle, of which a special instance can be discerned in this game, we will...

      (pp. 504-586)

      56.1.1. Our considerations have reached the stage at which it is possible to drop the zero-sum restriction for games. We have already relaxed this condition once to the extent of considering constant-sum games—with a sum different from zero. But this was not a really significant extension of the zero-sum case since these games were related to it by the isomorphism of strategic equivalence (cf. 42.1. and 42.2.). We now propose to go the whole way and abandon all restrictions concerning the sum.

      We pointed out before that the zero-sum restriction weakens the connection between games and economic problems quite...

      (pp. 587-616)

      65.1.1. Our mathematical considerations of then-person game beginning with the definitions of 30.1.1. made use of the concepts of imputation, domination and solution, which were then unambiguously established. Nevertheless in the subsequent development of the theory there occurred repeatedly instances where these concepts underwent variations. These instances were of three kinds:

      First: It happened in the course of our mathematical deductions, based strictly on the original definitions, that concepts rose to importance which were obviously analogous to the original ones (of imputation, domination, solution) but not exactly identical with them. In this case it was convenient to designate them...

      (pp. 617-632)
  5. Afterword
    (pp. 633-636)

    During the past ten years Princeton University Press has done a remarkable job of republishing, in a beautiful and eye-catching format, many of the seminal works from the early days of game theory at Princeton. This new printing ofTheory of Games and Economic Behavior, marking the book’s sixtieth anniversary, continues the celebration of game theory. Since the original publication of the book, game theory has moved from the fringe of economics into its mainstream. The distinction between economic theorist and game theorist has virtually disappeared. The 1994 Nobel Prize awarded to John Nash, John Harsanyi, and Reinhard Selten was...


    • The American Journal of Sociology
      (pp. 637-640)
    • Bulletin of the American Mathematical Society
      (pp. 640-646)
    • The American Economic Review
      (pp. 646-664)
    • Economica
      (pp. 664-667)
    • Pyschometrika
      (pp. 667-674)
  7. Heads, I Win, and Tails, You Lose
    (pp. 675-677)

    This classic in the history of intellectual thought is now 20 years old and available in paperback form. Representing the collaboration of a mathematical genius and a gifted economist, the book not only has provided aesthetic delight to thousands of readers and a fertile field for subsequent mathematical research but also it has provided direct stimulus to the related fields of personal probability. decision-making in statistics and operations research, linear programming and more general optimizing. Indeed the book has accomplished everything except what it started out to do-namely, revolutionize economic theory.

    Nevertheless,Theory of Gamesis a work of genius...

  8. Big D
    (pp. 678-679)

    As we predicted some time back, King Hill made All-America, and now this column is finally and flatly going out of the sports prediction business. You can push this psychic stuff just so far before the ghosts rebel.

    For a long time, though, we have meant to do a piece on the science of predicting generally. A mathematical genius named von Neumann has already tried it. He wrote a book called theTheory of Games, which is a best seller among five or six people these days. As we get his theory, if something happens once in five times and...

  9. Mathematics of Games and Economics
    (pp. 680-682)

    This book is based on the theory that the economic man attempts to maximize his share of the world’s goods and services in the same way that a participant in a game involving many players attempts to maximize his winnings. The authors point out that the maximization of individual wealth is not an ordinary problem in variational calculus, because the individual does not control, and may even be ignorant of, some of the variables. The general theory of social games, in their view, offers a simplified conceptual model of economic behaviour, and a study of that theory, can do much...

  10. Theory of Games
    (pp. 683-685)

    Attempts to apply mathematical methods in economics have been frequent, but until now not altogether successful. The reason for this, according to J. von Neumann and O. Morgenstern, is that too often one has tried to follow the pattern indicated by the mechanical or physical theories, where the spotlight is taken by differential equations expressing the immediate future of a system in terms of its present condition. The approach of the present authors is radically different; they treat economical life as a game played by a finite number of players according to certain rules, and they investigate the possible types...

  11. Mathematical Theory of Poker Is Applied to Business Problems
    (pp. 686-691)

    A new approach to economic analysis that seeks to solve hitherto insoluble problems of business strategy by developing and applying to them a new mathematical theory of games of strategy like poker, chess and solitaire has caused a sensation among professional economists.

    The theory has been worked out in its beginnings by Dr. John von Neumann, Professor of Mathematics at the Institute for Advanced Study, Princeton, N. J., and Dr. Oskar Morgenstern, Professor of Economics at Princeton University. In its present form the theory represents fifteen years of research, apart from the years spent by Dr. von Neumann before 1928...

  12. A Theory of Strategy
    (pp. 692-711)

    In the Spartan surroundings of a Pentagon office a young scientist attached to the Air Force said, “We hope it will work, just as we hoped in 1942 that the atomic bomb would work.” What he hoped and in some sense implied will work is a newly created theory of strategy that many scientists believe has important potentialities in military affairs, economics, and other social sciences. The theory is familiarly known to the military as “Games,” though its high security classification wherever it has actual content is a sign that its intent is anything but trifling. Before too much is...

  13. The Collaboration between Oskar Morgenstern and John von Neumann on the Theory of Games
    (pp. 712-726)

    Time and again since the publication of theTheory of Games and Economic Behaviorin 1944 the question has been asked how it came about that von Neumann, one of the greatest mathematicians of our age, and I met and worked together on what turned out to be a major piece in both our lives [20, (1944) 1953]. Recently I have been pressed by many to set down the history of the collaboration. And so I shall try to give a brief account of our mutual involvement. A fuller account with precise dates may follow some other time.

    My first...

  14. Index
    (pp. 727-740)
    (pp. 741-741)