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On the existence of maximal elements: An impossibility theorem

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  • Nikolai S Kukushkin

    (Russian Academy of Sciences Dorodnicyn Computing Center)

Abstract

Most 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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File URL: http://128.118.178.162/eps/game/papers/0509/0509004.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Game Theory and Information with number 0509004.

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Length: 7 pages
Date of creation: 28 Sep 2005
Date of revision:
Handle: RePEc:wpa:wuwpga:0509004

Note: Type of Document - pdf; pages: 7
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Web page: http://128.118.178.162

Related research

Keywords: Binary relation; Maximal element; Necessary and sufficient condition; Potential games;

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  1. Campbell, Donald E. & Walker, Mark, 1990. "Maximal elements of weakly continuous relations," Journal of Economic Theory, Elsevier, vol. 50(2), pages 459-464, April.
  2. Mukherji, Anjan, 1977. "The Existence of Choice Functions," Econometrica, Econometric Society, vol. 45(4), pages 889-94, May.
  3. 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.
  4. Bergstrom, Theodore C., 1975. "Maximal elements of acyclic relations on compact sets," Journal of Economic Theory, Elsevier, vol. 10(3), pages 403-404, June.
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Cited by:
  1. 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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