In the 1970s, mathematical economists worked to establish rigorous microfoundations for widely used equilibrium models, on the basis of the assumption that individuals are utility-maximizing rational agents (the "utility hypothesis"). It was already known that this assumption put certain loose restrictions on the excess demand functions for individuals (continuity and Walras's law), and that these restrictions were "inherited" by the market excess demand function. In a 1973 paper, Hugo Sonnenschein posed the question of whether these were the only restrictions that could be placed on a market excess demand function. He conjectured that the answer was "yes," and made preliminary steps toward proving it. These results were extended by Rolf Mantel, and then by Gérard Debreu in 1974, who proved that, as long as there are at least as many agents in the market as there are commodities, the market excess demand function inherits only the following properties of individual excess demand functions:
