## An Instant Classic Revisited

**October 26, 2004**

**Book ReviewJames Case**

**Theory of Games and Economic Behavior (Sixtieth Anniversary Edition).** *By John von Neumann and Oskar Morgenstern, Princeton University Press, Princeton, New Jersey, 2004, xxxii + 739 pages, $50.00.*

During the past ten years, Princeton University Press has published new editions (in attractive format, on high-quality acid-free paper) of a number of notable books and papers on game theory. The volume under review includes all xx + 641 pages of the third (1953) edition of von Neumann and Morgenstern's instant classic, first published in September 1944 (hereinafter abbreviated TGEB). The extra xii + 98 pages contain a new introduction by Harold Kuhn, a new afterword by Ariel Rubinstein, a fifteen-page account by Morgenstern of his collaboration with von Neumann, and a number of opinion pieces about the ultimate place of the book in intellectual history.

Kuhn's introduction echoes, among other things, R.J. Leonard's surmise that "had von Neumann and Morgenstern never met, it seems unlikely that game theory would have been developed." Such a conclusion is difficult to reconcile with the well-documented fact that development of the theory began before either von Neumann or Morgenstern was born, and seemed to be gathering momentum by the time of von Neumann's landmark 1928 paper proving the minimax theorem and a generalization of Zermelo's perfect information theorem. By then, special cases of both von Neumann's theory of matrix games and John Nash's noncooperative theory of many-player games had been described in the open literature. Moreover, in the 1928 paper von Neumann dealt briefly with three-player games and provided at least a preview of the cooperative theory that he and Morgenstern would develop later. What seems undeniable is that the theory would have developed much more slowly, with far less fanfare, and *very differently* had the two never met.

Kuhn is unduly modest in describing his own involvement in the early development of game theory. It seems that, in the fall of 1947 and again in the spring of 1948, George Dantzig visited Princeton to discuss linear programming with von Neumann. At the end of the second visit, as A.W. Tucker was driving Dantzig to the train station, the suggestion emerged that the research proposed by Dantzig to von Neumann on the connection between linear programming and matrix game theory be done at Princeton. Within the month, Tucker had secured funding from the Navy to hire Kuhn and David Gale for the summer---time enough for the three to teach one another game theory and demonstrate the equivalence of linear programming and matrix games.

Enthused by the research potential of the subject they had just learned, the three initiated a weekly seminar on game theory for the following fall. Present from time to time were von Neumann, Morgenstern, and other members of the Princeton faculty, visitors to the Institute for Advanced Study, including Ky Fan and Irving Kaplansky, Columbia statistician Abraham Wald, and newly arrived graduate students John Nash, Lloyd Shapley, and Martin Shubik. Wald already had done, and the rest would later do, important research in game theory. The famous Kuhn-Tucker conditions of mathematical programming were yet another by-product of that fruitful summer project.

Kuhn lists a dozen reviews of TGEB, published between 1945 and 1950. They average 14+ pages in length, appeared in leading journals of mathematics and/or the social sciences, and were written by already or soon-to-be prominent authors. Two of the latter, H.A. Simon and J.R.N. Stone, went on to win Nobel Memorial Prizes in Economics. Any author (or publisher) would kill for such reviews, four of which are reproduced in the anniversary edition. Even today, they make interesting reading. One of them, paraphrased by a reporter on the first page of the *New York Times* book section on March 10, 1946, caused the first edition of the book to sell out a short time later. A second edition, differing little from the first, appeared the following year. Kuhn makes the point that, enthusiastic though the early reviewers of TGEB were, none of them ever did research in game theory.

The other commentaries on TGEB included in the anniversary edition range from a moderately amusing spoof written in 1957 by a one-time sportswriter named Paul Crume to a three-page synopsis by mathematician Claude Chevalley (1945) to a twenty-page exposition by *Fortune* magazine writer John McDonald (1949). Perhaps the most telling is economist Paul Samuelson's three-page appreciation from the 1960s describing TGEB as "a work of genius" that "has accomplished everything except what it started out to do---namely, revolutionize economic theory."

In his afterword, Ariel Rubinstein echoes Samuelson's skepticism, pointing out that there "are very few insights from game theory that would improve one's game of chess or poker" and that, sixty years after publication, it can claim few if any accurate economic predictions. While conceding that game theory has enriched popular discourse with terms like "zero-sum" and "prisoner's dilemma," Rubinstein observes that the former serves mainly to demonstrate the speaker's level of sophistication---or lack thereof---and the latter expresses only the obvious fact that "there are situations in which selfish behavior can harm all participants."

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 pages---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 writes from Baltimore, Maryland.*