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John von Neumann (born December 28, 1903 in Hungary, died February 8, 1957 in Washington, D.C.) was a versatile scholar whose path-breaking ideas have enriched various disciplines. In social sciences his contributions to game theory, economic growth, and consumers’ choice are of special importance.
Von Neumann’s talents showed up early, and outstanding mathematicians tutored him individually. In 1923 he entered MSc chemistry studies in Zurich and at the same time studied for a doctoral degree in mathematics in Budapest. In 1926 and 1927, as an assistant to David Hilbert in Gottingen, he laid down the axiomatic foundations of quantum mechanics. His reputation grew rapidly, and he was invited to several universities. He visited Princeton University first in 1929 and became a professor of mathematics at its Institute for Advanced Study in 1933. He became a leading expert on shock and detonation waves, which became significant during World War II (1939-1945), when von Neumann became involved in important projects such as the Manhattan Project. It was mainly the complex nonlinear problems that emerged in these projects that made him realize the importance of computers, and he made key contributions to formulating the basic principles of computer science.
Von Neumann made major scientific contributions to the social sciences as well. As always, he was interested in comprehensive structures, and focused on the core problems in the field. He was the first to prove the existence of equilibrium for two-person zero-sum games in 1928, based on his famous minimax theorem. Using a similar mathematical structure he formulated a multisectoral model of balanced economic growth (first presented in 1932), which was a brilliant mathematical synthesis of some classical ideas concerning the production and price proportions of economic equilibrium. He was the first to employ a fixed-point theorem in the proof of existence of competitive equilibrium, on the one hand, and an explicit duality approach, recognizing the symmetry of the conditions that characterize the choice of optimal activities and the equilibrium price system sustaining it under the conditions of a competitive equilibrium, on the other. His model allows for different theoretical interpretations (classical, Marxist, neoclassical, etc.) indicating its general nature.
Although his model was a prototype of the highly abstract models used in modern economics, he cautioned often against the potential deterioration of such an approach into intellectual games. He saw this danger threatening not only the development of economics but also mathematics itself. He repeatedly criticized economists for not using more appropriate mathematics, and he emphasized the need for more comprehensive tools than those borrowed from classical physics.
Von Neumann set an excellent example for such a novel approach in his work with Oskar Morgenstern on game theory. In their book, Theory of Games and Economic Behavior (1944), they laid down the foundations of modern game theory and initiated a new discipline almost from scratch. It was in this connection that they developed the axiomatic theory of expected utility, which states that under certain conditions the preferences of a rational individual can be represented by a function of the expected utility form. The use of the von Neumann-Morgenstern expected utility function became universal in economics because it is analytically very convenient and its normative character may provide a valuable guide to rational actions. Although he darted only briefly into its domain, von Neumann’s tremendous influence on the development of modern economics has been widely acknowledged.
Bibliography:
- Von Neumann, John. 1945. A Model of General Economic Equilibrium. Review of Economic Studies 13: 1–9. (Published first in German, 1937.)
- Von Neumann, John, and Oskar Morgenstern. 1944. Theory of Games and Economic Behavior. Princeton, NJ: Princeton University Press.
- Zalai, Erno, guest ed. 2004. A Special Issue on John von Neumann. Acta Oeconomica 54 (1): 1–96.
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