On the existence of approximated equilibria in discontinuous economies

In this paper, we prove an existence theorem for approximated equilibria in a class of discontinuous economies. The existence result is a direct consequence of a discontinuous extension of Brouwer’s fixed point Theorem (1912), and is a refinement of several classical results in the standard general equilibrium with incomplete markets (GEI) model. [Brouwer, L.E.J., 1912. Über Abbildung von Mannigfaltigkeiten. Mathematische Annalen 71, 97–115.] As a by-product, we get the first existence proof of an approximated equilibrium in the GEI model, without perturbing the asset structure nor the endowments. Our main theorem rests on a new topological structure result for the asset equilibrium space and may be of interest by itself.