On the existence of approximated equilibria in discontinuous economies
Bich, Philippe (2005), On the existence of approximated equilibria in discontinuous economies, Journal of Mathematical Economics, 41, 4-5, p. 463-481. http://dx.doi.org/10.1016/j.jmateco.2004.12.003
TypeArticle accepté pour publication ou publié
Journal nameJournal of Mathematical Economics
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Abstract (EN)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.
Subjects / KeywordsGeneral equilibrium; Incomplete markets; Discontinuity; Fixed point
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