The "Vienna Colloquium" run by the mathematician Karl Menger (son of the economist Carl Menger) in the 1930s, brought together many different minds from mathematics but also the physical sciences, philosophy, statistics and economics, that eventually set in motion modern general equilibrium theory from its early roots in the Lausanne School.
Among the relevant participants in the Colloquium besides Karl Menger, was the banker and amateur economist Karl Schlesinger as well as the young Oskar Morgenstern, the polymath John von Neumann and the statistician Abraham Wald. Other participants included assorted Viennese physicists and mathematicians like Kurt Gödel. The proceedings of the Colloquium were collected by Menger and published as the Ergebnisse eines mathematischen Kolloquiums during the 1930s.
One could argue that the Vienna Colloquium was the product of three distinct intellectual strands: the logical positivist philosophy of the Vienna Circle, the mathematics of Hilbert's "formalist" programme and the economics of the Austrian School. In economics, the rallying point for the Vienna Colloquium was the investigation of metatheoretic general equilibrium systems with multiple, simultaneously interacting parts. For economists, the prototype of such a system was Gustav Cassel's (1918) resurrection of Leon Walras's theory, presentation of what has since become known as the Walras- Cassel model. The critiques set forth in the late 1920s and early 1930s by Frederik Zeuthen, Hans Neisser, Heinrich von Stackelberg on the Walras-Cassel system - particularly in relation to the possible existence of negative prices and indeterminacy arising from the equalities assumed by Leon Walras and Gustav Cassel.
The solution provided by the Vienna Colloquium, namely the introduction of complementary "slackness" conditions was first proposed by Schlesinger. After a few attempts, Abraham Wald (1935, 1936) finally provided the first "existence" proof of a unique equilibrium for the static Walras-Cassel system with inequalities exploiting these complementary slackness conditions and introducing the weak axiom of revealed preference. John von Neumann's (1937) model of an expanding multi-sectoral economy was closer in spirit to the Classical Ricardian than the Walrasian general equilibrium world, but it provided a proof of existence via a generalization of Brouwer's fixed point theorem, the characterization of a solution as a saddle-point and the first to specify and exploit programming "duality" theorems and slackness conditions more fully.
Another outgrowth of the Vienna Colloquium was the axiomatization of utility theory, the introduction of uncertainty into the theory of choice and the development of the theory of games. This was pursued by two of its participants, John von Neumann and Oskar Morgenstern, in their pathbreaking treatise Theory of Games and Economic Behavior, which, although only published in 1944 while they were both in Princeton, clearly had its roots in the Vienna Colloquium (e.g. Bernoulli's expected utility hypothesis was introduced to John von Neumann through Karl Menger's 1934 article).
The Vienna Colloquium was disbanded in 1938 after the German invasion and most of its members were scattered in exile in Britain and the United States. Although it was never resurrected, much of its research programme was taken up in the 1940s and 1950s by the Cowles Commission in Chicago.
The Vienna Colloquium Participants
Resources Karl Menger's Vienna Colloquium
