On the existence of approximated equilibria in discontinuous economies

Philippe Bich ()
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Philippe Bich: CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique

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Abstract: 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 (e.g., Bottazzi (1995), Duffie and Shafer (1985), Husseini et al. (1990), Geanakoplos and Shafer (1990), Magill and Shafer (1991)). 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.

Keywords: general equilibrium; incomplete markets; approximated equilibrium (search for similar items in EconPapers)
Date: 2005-08
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00287685
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Published in Journal of Mathematical Economics, 2005, 41 (4-5), pp.463-481. ⟨10.1016/j.jmateco.2004.12.003⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-00287685

DOI: 10.1016/j.jmateco.2004.12.003

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