General conditions for the existence of maximal elements via the uncovered set
This paper disentangles the topological assumptions of classical results (e.g.,Walker, 1977 on the existence of maximal elements from rationality conditions. It is known from the social choice literature that under the standard topological conditions—with no rationality assumptions on preferences—there is an element such that the upper section of strict preference at that element is minimal in terms of set inclusion, i.e., the uncovered set is nonempty. Assuming the finite subordination property, a condition that weakens known acyclicity and convexity assumptions, each such uncovered alternative is in fact maximal. Implications are a generalization of a result of Yannelis and Prabhakar (1983) on semi-convexity, an extension of Fan’s (1961) lemma on KKM correspondences, and the existence of fixed points for subordinate convex correspondences generalizing the work of Browder (1968).
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Volume (Year): 47 (2011)
Issue (Month): 6 ()
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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.:
- SCHMEIDLER, David, .
"Competitive equilibria in markets with a continuum of traders and incomplete preferences,"
CORE Discussion Papers RP
62, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Schmeidler, David, 1969. "Competitive Equilibria in Markets with a Continuum of Traders and Incomplete Preferences," Econometrica, Econometric Society, vol. 37(4), pages 578-85, October.
- Jeffrey S. Banks & John Duggan & Michel LeBreton, .
"Bounds for Mixed Strategy Equilibria and the Spatial Model of Elections,"
Wallis Working Papers
WP14, University of Rochester - Wallis Institute of Political Economy.
- Banks, Jeffrey S. & Duggan, John & Le Breton, Michel, 2002. "Bounds for Mixed Strategy Equilibria and the Spatial Model of Elections," Journal of Economic Theory, Elsevier, vol. 103(1), pages 88-105, March.
- Schofield, Norman, 1984.
"Social equilibrium and cycles on compact sets,"
Journal of Economic Theory,
Elsevier, vol. 33(1), pages 59-71, June.
- Tian, Guoqiang & Zhou, Jianxin, 1995. "Transfer continuities, generalizations of the Weierstrass and maximum theorems: A full characterization," Journal of Mathematical Economics, Elsevier, vol. 24(3), pages 281-303.
- Nehring, Klaus, 1996. "Maximal elements of non-binary choice functions on compact sets," Economics Letters, Elsevier, vol. 50(3), pages 337-340, March.
- Mas-Colell, Andrew, 1974. "An equilibrium existence theorem without complete or transitive preferences," Journal of Mathematical Economics, Elsevier, vol. 1(3), pages 237-246, December.
- Yannelis, Nicholas C., 1985. "Maximal elements over non-compact subsets of linear topological spaces," Economics Letters, Elsevier, vol. 17(1-2), pages 133-136.
- Bergstrom, Theodore C., 1975. "Maximal elements of acyclic relations on compact sets," Journal of Economic Theory, Elsevier, vol. 10(3), pages 403-404, June.
- Walker, Mark, 1977. "On the existence of maximal elements," Journal of Economic Theory, Elsevier, vol. 16(2), pages 470-474, December.
- Alcantud, Jose C.R., 2006.
"Maximality with or without binariness: Transfer-type characterizations,"
Mathematical Social Sciences,
Elsevier, vol. 51(2), pages 182-191, March.
- J C R Alcantud, 2004. "Maximality with or without binariness: transfer-type characterizations," Microeconomics 0402015, EconWPA.
- Shafer, Wayne & Sonnenschein, Hugo, 1975.
"Equilibrium in abstract economies without ordered preferences,"
Journal of Mathematical Economics,
Elsevier, vol. 2(3), pages 345-348, December.
- Wayne Shafer & Hugo Sonnenschein, 1974. "Equilibrium in Abstract Economies Without Ordered Preferences," Discussion Papers 94, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Yannelis, Nicholas C. & Prabhakar, N. D., 1983. "Existence of maximal elements and equilibria in linear topological spaces," Journal of Mathematical Economics, Elsevier, vol. 12(3), pages 233-245, December.
- Banks, Jeffrey & Duggan, John & Le Breton, Michel, 2003.
"Social Choice and Electoral Competition in the General Spatial Model,"
IDEI Working Papers
188, Institut d'Économie Industrielle (IDEI), Toulouse.
- Banks, Jeffrey S. & Duggan, John & Le Breton, Michel, 2006. "Social choice and electoral competition in the general spatial model," Journal of Economic Theory, Elsevier, vol. 126(1), pages 194-234, January.
- Peris, Josep E. & Subiza, Begona, 1994.
"Maximal elements of not necessarily acyclic binary relations,"
Elsevier, vol. 44(4), pages 385-388, April.
- Josep Enric Peris Ferrando & Begoña Subiza Martínez, 1992. "Maximal elements of non necessarily acyclic binary relations," Working Papers. Serie AD 1992-07, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
- Campbell, Donald E. & Walker, Mark, 1990. "Maximal elements of weakly continuous relations," Journal of Economic Theory, Elsevier, vol. 50(2), pages 459-464, April.
- Donald J. Brown, 1973. "Acyclic Choice," Cowles Foundation Discussion Papers 360, Cowles Foundation for Research in Economics, Yale University.
- John Duggan, 2011. "Uncovered Sets," Wallis Working Papers WP63, University of Rochester - Wallis Institute of Political Economy.
- Horvath, Charles D. & Ciscar, Juan Vicente Llinares, 1996. "Maximal elements and fixed points for binary relations on topological ordered spaces," Journal of Mathematical Economics, Elsevier, vol. 25(3), pages 291-306.
- Pavlo Prokopovych, 2011. "On equilibrium existence in payoff secure games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(1), pages 5-16, September.
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