John von Neumann's contribution to economic science

International Social Science Review, Fall-Winter, 2003 by Maria Joao Cardoso De Pina Cabral

In the fall of 1940, von Neumann wrote his first paper on games, "Theory of Games I, General Foundations," quickly followed by a second paper, delivered in January 1941, entitled, "Theory of Games II, Decomposition Theory." (54) In both papers, von Neuman tried to synthesize his work on game theory. (55) Although these working papers do not list an author, the mathematical style and the fact that Morgenstern placed the papers in a folder which included other works written by von Neumann indicates that he was the author. Then, on May 17, 1941, von Neumann asked Morgenstern to write a paper on 'maxims of behavior,' a frequent topic of interest throughout their discussions. Although never published, this paper, entitled "Quantitative Implications of Maxims of Behavior" apparently had a direct impact on von Neumann's decision to collaborate with Morgenstern. Initially this collaboration was expected to produce a fifty-page manuscript for submission to the Journal of Political Economy. It would later be expanded into a pamphlet (approximately 100 pages), then a short book, and finally a book that exceeded 600 pages. (56)

The issue of von Neumann-Morgenstern's collaboration has been a subject of much discussion. The fact that Morgenstern wrote about this collaboration in his diary helps in determining the contribution of each author. In the first place, the asymmetry between von Neumann and Morgenstern in their collaboration is obvious. (57) Their names are not listed in alphabetical order on the cover of the book. (58) Additionally, the preface states that "the theory had been developed by one of them since 1928." (59) Yet, while it is quite clear that von Neumann was indispensable for the progress of the work, (60) Morgenstern's contribution proved crucial. He brought to the theory of games the other stream of work recognized, in retrospect, as analysis of games, developed by Antoine August Cournot's economic contribution on duopoly, and the work of Eugene Bohm-Bawerk. (61)

The Theory of Games and Economic Behavior (TGEB) represents the emergence of game theory as a distinct recognized discipline. Although economics was a central concern for the authors, the scope of the book extended far beyond economics, reaching political science and sociology. In the first chapter, which provides the economic context for game theory, the authors advanced axiomatization of the measurable utility, one of the most important contributions of the book to the study of economics. Using Bernoulli's analysis (62) as their starting point, they established a system of axioms for a numerical utility and achieved the 'von Neumann-Morgenstern utility function.' This represented an essential advance in general demand theory, particularly under risk and uncertainty situations. (63)

Another major contribution of TGEB is the concept of static economic equilibrium. Although the application of this concept is model-dependent, it does not require any particular 'rules of the game.' Thus, von Neumann and Morgenstern's equilibrium solution, contrary to previous treatments such as the general competitive equilibrium of Marie-Espirit Leon Walrus, Vilfredo Pareto, and Irving Fisher, does not depend on perfect competition, or, even, on market contexts, which limited interaction. (64)