Gérard Debreu (4 July 1921 – 31 December 2004) was a French-born American economist and mathematician. Best known as a professor of economics at the University of California, Berkeley, where he began work in 1962, he won the 1983 Nobel Memorial Prize in Economic Sciences.
In 1959, he published his classical monograph, Theory of Value: An Axiomatic Analysis of Economic Equilibrium (Cowles Foundation Monographs Series), which is one of the most important works in mathematical economics. He also studied several problems in the theory of cardinal utility, in particular the additive decomposition of a utility function defined on a Cartesian product of sets.
In this monograph, Debreu set up an axiomatic foundation for competitive markets. He also established the existence of an equilibrium using a novel approach. The main idea of his argument is to show that there exists a price system for which the aggregate excess demand correspondence vanishes. He did so by proving a type of fixed-point theorem that is based on the Kakutani fixed-point theorem. In Chapter 7, Debreu introduced the concept of uncertainty and showed how it could be incorporated into the deterministic model. Here, he introduced the notion of a contingent commodity, which is a promise to deliver a good should a certain state of nature be realized. This concept is very frequently used in financial economics, where it is known as the “Arrow–Debreu security”.
In 1960–61, he worked at the Center for Advanced Study in the Behavioral Sciences at Stanford and devoted most of his time to the complex proof that appeared in 1962 of a general theorem on the existence of an economic equilibrium.