## Theory of Games and Economic Behavior.

Princeton: Princeton University Press, 1944.

First edition, and a fine copy with the very rare dust jacket, of “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 ground-breaking 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” (from the introduction to the 60th anniversary commemorative edition). Von Neumann’s “role as founder is even more obvious for the theory of games, which von Neumann, in a 1926 paper, conjured—so to speak—out of nowhere. To give a quantitative mathematical model for games of chance such as poker or bridge might have seemed a priori impossible, since such games involve free choices by the players at each move, constantly reacting on each other. Yet von Neumann did precisely that, by introducing the general concept of ‘strategy’ (qualitatively considered a few years earlier by E. Borel) and by constructing a model that made this concept amenable to mathematical analysis. That this model was well adapted to the problem was shown conclusively by von Neumann in the same paper, with the proof of the famous minimax theorem: for a game with two players in a normalized form, it asserts the existence of a unique numerical value, representing a gain for one player and a loss for the other, such that each can achieve at least this favorable expectation from his own point of view by using a ‘strategy’ of his own choosing; such strategies for the two players are termed optimal strategies, and the unique numerical value, the minimax value of the game. This was the starting point for far-reaching generalizations, including applications to economics, a topic in which von Neumann became interested as early as 1937 and that he developed in his major treatise written with O. Morgenstern. *Theory of Games and Economic Behavior* (1944)” (DSB). Only two copies of this book with the dust jacket are listed on ABPC/RBH (PBA, 22 February, 2007, “sizable piece missing from spine”; and the Norman copy, Christie’s, 29 October 1998).

“Quantitative mathematical models for games such as poker or bridge at one time appeared impossible, since games like these involve free choices by the players at each move, and each move reacts to moves of other players. However, in the 1920s John von Neumann single-handedly invented game theory, introducing the general mathematical concept of ‘strategy’ in a paper on games of chance [‘Zur Theorie der Gesellschaftsspiele,’ *Mathematische Annalen* 100, 1928]. This contained the proof of his ‘minimax’ theorem that says ‘a strategy exists that guarantees, for each player, a maximum payoff assuming that the adversary acts so as to minimize that payoff.’ The ‘minimax’ principle, a key component of the game-playing computer programs developed in the 1950s and 1960s by Samuel, Newell, Simon, and others, was more fully articulated and explored in ‘The Theory of Games and Economic Behavior’, co-authored by von Neumann and the Austrian economist Oskar Morgenstern. Game theory, which draws upon mathematical logic, set theory and functional analysis, attempts to describe in mathematical terms the decision-making strategies used in games and other competitive situations. … Von Neumann revolutionized mathematical economics. Had he not suffered an early death from cancer in 1957, he most probably would have received the Noble Prize in economics. Several mathematical economists influenced by von Neumann’s ideas [as Nash, Harsanyi and Selten] later received the Nobel Prize in Economics” (Hook & Norman, *Origins of Cyberspace*, p. 473).

“Of the many areas of mathematics shaped by his genius, none shows more clearly the influence of John von Neumann than the Theory of Games. This modern approach to problems of competition and cooperation was given a broad foundation in his superlative paper of 1928. In scope and youthful vigor this work can be compared only to his papers of the same period on the axioms of set theory and the mathematical foundations of quantum mechanics. A decade later, when the Austrian economist Oskar Morgenstern came to Princeton, von Neumann's interest in the theory was reawakened. The result of

their active and intensive collaboration during the early years of World War II was the treatise Theory of games and economic behavior, in which the basic structure of the 1928 paper is elaborated and extended. Together, the paper and treatise contain a remarkably

complete outline of the subject as we know it today, and every writer in the field draws in some measure upon concepts which were there united into a coherent theory.

“The crucial innovation of von Neumann, which was to be both the keystone of his Theory of Games and the central theme of his later research in the area, was the assertion and proof of the Minimax Theorem. Ideas of pure and randomized strategies had been introduced earlier, especially by Êmile Borel. However, these efforts were restricted either to individual examples or, at best, to zero-sum two-person games with skew-symmetric payoff matrices. To paraphrase his own opinion, von Neumann did not view

the mere desire to mathematize strategic concepts and the straight formal definition of a pure strategy as the main agenda of an ‘initiator’ in the field, but felt that there was nothing worth publishing until the Minimax Theorem was proved …

“For any finite zero-sum two-person game in a normalized form, [the Minimax Theorem] asserts the existence of a unique numerical value, representing a gain for one player and a loss for the other, such that each can achieve at least this favorable an expectation from his own point of view by using a randomized (or mixed) strategy of his own choosing. Such strategies for the two players are termed optimal strategies and the unique numerical value, the minimax value of the game. This is the starting point of the von

Neumann-Morgenstern solution for cooperative games, where all possible partitions of the players into two coalitions are considered and the reasonable aspirations of the opposing coalitions in each partition measured by the minimax value of the strictly competitive two-party struggle between them. In the area of extensive games, the solution of games with perfect information by means of pure strategies assumes importance only by contrast to the necessity of randomizing in the general case. The Minimax Theorem reappears in a new guise, when von Neumann turned to analyze a linear model of production. Finally, in the hands of von Neumann, it was the source of a broad spectrum of technical results, ranging from his extensions of the Brouwer fixed-point theorem, developed for its proof, to new and unexpected methods for combinatorial problems …

“The impact of von Neumann's Theory of Games extends far beyond the boundaries of this subject. By his example and through his accomplishments, he opened a broad new channel of two-way communication between mathematics and the social sciences. These sciences were fortunate indeed that one of the most creative mathematicians of the twentieth century concerned himself with some of their fundamental problems and constructed strikingly imaginative and stimulating models with which to attack their problems quantitatively. At the same time, mathematics received a vital infusion of fresh ideas and methods that will continue to be highly productive for many years to come. Von Neumann's interest in “problems of

organized complexity,” so important in the social sciences, went hand in hand with his pioneering development of large-scale high-speed computers. There is a great challenge for other mathematicians to follow his lead in grappling with complex systems in many areas of the sciences where mathematics has not yet penetrated deeply” (Kuhn & Tucker, ‘John von Neumann’s work in the theory of games and mathematical economics,’ *Bulletin of the American Mathematical Society* 64 (1958), pp. 100-122).

“Von Neumann (1903-57) may have been the last representative of a once-flourishing and numerous group, the great mathematicians who were equally at home in pure and applied mathematics and who throughout their careers maintained a steady production in both directions. Pure and applied mathematics have now become so vast and complex that mastering both seems beyond human capabilities. In von Neumann’s generation his ability to absorb and digest an enormous amount of extremely diverse material in a short time was exceptional; and in a profession where quick minds are somewhat commonplace, his amazing rapidity was proverbial. There is hardly a single important part of the mathematics of the 1930’s with which he had not at least a passing acquaintance, and the same is probably true of theoretical physics” (DSB, under Von Neumann).

The German-born economist Morgenstern (1902-77) taught at the University of Vienna from 1929. Although not Jewish, Morgenstern in 1938 was deemed to be politically unacceptable, and he therefore left Austria for the United States, where he was appointed as a lecturer in economics at Princeton University. He gravitated to the Institute for Advanced Study, where he met Von Neumann. “In the best sense of the term, Morgenstern must be regarded as a great entrepreneur in the development of economics in general and game theory in particular. There has always been considerable skepticism concerning his role in the development of game theory. An unverified story has a mathematician ask von Neumann, ‘What was Oskar Morgenstern’s contribution to the Theory of Games?’ Von Neumann is said to have replied: ‘Without Oskar, I would have never written the *Theory of Games and Economic Behavior*.’ This anecdote appears to reflect the fact that although Morgenstern’s mathematical abilities were quite limited, when he recognized an important idea that could be mathematized, he persisted in finding mathematical collaboration” (DSB, under Morgenstern)

OOC 953 [lacking jacket]; Norman 2167. For a detailed account of the genesis of this work, see Robert Leonard, *Von Neumann, Morgenstern, and the Creation of Game Theory*:* From Chess to Social Science, 1900-1960**,* 2012.

8vo (234 x 155 mm), pp. XVIII, 625, [1]. Errata sheet loosely inserted, as issued. Original cloth with dust jacket, binding tight and clean, jacket with some small chips and tears to the extremities, not sunned or faded. A fine copy, completely clean and fresh throughout.

Item #5195

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Price:
$12,500.00
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