Abstract
A new proof of the existence of a Walrasian equilibrium with an infinite dimensional commodity space is provided, which allows agents’ preferences to be discontinuous. The new theorems include as corollaries the existence results of Mas-Collel, Yannelis and Zame, Araujo and Monteiro, and Mas-Collel and Richard, among others.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Aliprantis, C.D., Burkinshaw, O.: Equilibria in markets with a Riesz space of commodities. J. Math. Econ. 11, 189–207 (1983)
Anderson, R.M., Duanmu, H., Khan, M.A., et al.: Walrasian equilibrium theory with and without free disposal: theorems and counterexamples in an infinite-agent context. Econ. Theory 73, 387–412 (2022). https://doi.org/10.1007/s00199-021-01395-0
Araujo, A., Monteiro, P.K.: Equilibrium without uniform conditions. J. Econ. Theory 48, 416–427 (1989)
Bewley, T.F.: Existence of equilibria in economies with infinitely many commodities. J. Econ. Theory 4(3), 514–540 (1972)
Dasgupta, P., Maskin, E.: The existence of equilibrium in discontinuous economic games, I: theory. Rev. Econ. Stud. 53, 1–26 (1986)
Engelking, R.: General Topology, Sigma Series in Pure Mathematics, vol. 6. Heldermann Verlag, Berlin (1989)
Gale, D., Mas-Colell, A.: An equilibrium existence theorem for a general model without ordered preferences. J. Math. Econ. 2, 9–16 (1975)
He, W., Yannelis, N.C.: Existence of Walrasian equilibria with discontinuous, non-ordered, interdependent and price-dependent preferences. Econ. Theory 61, 497–513 (2016). https://doi.org/10.1007/s00199-015-0875-x
He, W., Yannelis, N.C.: Equilibria with discontinuous preferences: New fixed point theorems. J. Math. Anal. Appl. 450(2), 1421–1433 (2017)
Hildenbrand, W.: Core and Equilibria of a Large Economy. Princeton University Press, Princeton (1974)
Mas-Colell, A.: The price equilibrium existence problem in topological vector lattices. Econometrica 54, 1039–1053 (1986)
Mas-Colell, A., Richard, S.F.: A new approach to the existence of equilibria in vector lattices. J. Econ. Theory 53, 1–11 (1991)
Podczeck, K.: Equilibria in vector lattices without ordered preferences or uniform properness. J. Econ. Theory 25, 465–485 (1996)
Podczeck, K., Yannelis, N.C.: Existence of Walrasian equilibria with discontinuous, non-ordered, interdependent and price-dependent preferences, without free disposal, and without compact consumption sets. Econ. Theory 73, 413–420 (2022)
Reny, P.J.: On the existence of pure and mixed strategy equilibria in discontinuous games. Econometrica 67, 1029–1056 (1999)
Reny, P.J.: Nash equilibrium in discontinuous games. Ann. Rev. Econ. 12, 439–470 (2020)
Shafer, W.J.: Equilibrium in economies without ordered preferences or free disposal. J. Math. Econ. 3, 135–137 (1976)
Yannelis, N.C., Zame, W.R.: Equilibria in Banach lattices without ordered preferences. J. Math. Econ. 15, 85–110 (1986)
Funding
Open access funding provided by University of Vienna.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
We thank two referees for helpful comments and suggestions. Any remaining errors are, of course, ours.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Podczeck, K., Yannelis, N.C. Existence of Walrasian equilibria with discontinuous, non-ordered, interdependent preferences, without free disposal, and with an infinite-dimensional commodity space. Econ Theory 78, 389–401 (2024). https://doi.org/10.1007/s00199-024-01553-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00199-024-01553-0
Keywords
- Continuous inclusion property
- Exchange economy
- Infinite-dimensional commodity space
- Existence of Walrasian equilibrium