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 (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.
|Date of creation:||Aug 2005|
|Publication status:||Published in Journal of Mathematical Economics, Elsevier, 2005, 41 (4-5), pp.463-481. <10.1016/j.jmateco.2004.12.003>|
|Note:||View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00287685|
|Contact details of provider:|| Web page: https://hal.archives-ouvertes.fr/|
References listed on IDEAS
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- Chichilnisky, Graciela & Heal, Geoffrey, 1996. "On the existence and the structure of the pseudo-equilibrium manifold," Journal of Mathematical Economics, Elsevier, vol. 26(2), pages 171-186.
- Hirsch, M. D. & Magill, M. & Mas-Colell, A., 1990. "A geometric approach to a class of equilibrium existence theorems," Journal of Mathematical Economics, Elsevier, vol. 19(1-2), pages 95-106.
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- Duffie, Darrell & Shafer, Wayne, 1985. "Equilibrium in incomplete markets: I : A basic model of generic existence," Journal of Mathematical Economics, Elsevier, vol. 14(3), pages 285-300, June.
- Magill, Michael & Shafer, Wayne, 1991. "Incomplete markets," Handbook of Mathematical Economics,in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 30, pages 1523-1614 Elsevier.
- Hart, Oliver D., 1975. "On the optimality of equilibrium when the market structure is incomplete," Journal of Economic Theory, Elsevier, vol. 11(3), pages 418-443, December.
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