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|
|Date of revision:|
|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
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Brown, Donald J & DeMarzo, Peter M & Eaves, B Curtis, 1996. "Computing Equilibria When Asset Markets Are Incomplete," Econometrica, Econometric Society, vol. 64(1), pages 1-27, January.
- Geanakoplos, John & Shafer, Wayne, 1990. "Solving systems of simultaneous equations in economics," Journal of Mathematical Economics, Elsevier, vol. 19(1-2), pages 69-93.
- Husseini, S. Y. & Lasry, J. -M. & Magill, M. J. P., 1990. "Existence of equilibrium with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 19(1-2), pages 39-67.
- Bottazzi, Jean-Marc, 1995. "Existence of equilibria with incomplete markets: The case of smooth returns," Journal of Mathematical Economics, Elsevier, vol. 24(1), pages 59-72.
- 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.
- 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.
- 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.
- 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.
When requesting a correction, please mention this item's handle: RePEc:hal:cesptp:halshs-00287685. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD)
If references are entirely missing, you can add them using this form.