On the existence of maximal elements: An impossibility theorem
AbstractMost properties of binary relations considered in the decision literature can be expressed as the impossibility of certain ``configurations.'' There exists no condition of this form which would hold for a binary relation on a subset of a finite-dimensional Euclidean space if and only if the relation admits a maximal element on every nonempty compact subset of its domain.
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Bibliographic InfoPaper provided by EconWPA in its series Game Theory and Information with number 0509004.
Length: 7 pages
Date of creation: 28 Sep 2005
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Note: Type of Document - pdf; pages: 7
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Binary relation; Maximal element; Necessary and sufficient condition; Potential games;
Find related papers by JEL classification:
- D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-10-04 (All new papers)
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- Smith, Tony E, 1974. "On the Existence of Most-Preferred Alternatives," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(1), pages 184-94, February.
- Mukherji, Anjan, 1977. "The Existence of Choice Functions," Econometrica, Econometric Society, vol. 45(4), pages 889-94, May.
- Campbell, Donald E. & Walker, Mark, 1990. "Maximal elements of weakly continuous relations," Journal of Economic Theory, Elsevier, vol. 50(2), pages 459-464, April.
- Bergstrom, Theodore C., 1975. "Maximal elements of acyclic relations on compact sets," Journal of Economic Theory, Elsevier, vol. 10(3), pages 403-404, June.
- Kukushkin, Nikolai S., 2008. "Maximizing an interval order on compact subsets of its domain," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 195-206, September.
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