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On the existence of maximal elements: An impossibility theorem

Author

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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.

Suggested Citation

  • Nikolai S Kukushkin, 2005. "On the existence of maximal elements: An impossibility theorem," Game Theory and Information 0509004, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpga:0509004
    Note: Type of Document - pdf; pages: 7
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/0509/0509004.pdf
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    References listed on IDEAS

    as
    1. Mukherji, Anjan, 1977. "The Existence of Choice Functions," Econometrica, Econometric Society, vol. 45(4), pages 889-894, May.
    2. 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 184-194, February.
    3. Campbell, Donald E. & Walker, Mark, 1990. "Maximal elements of weakly continuous relations," Journal of Economic Theory, Elsevier, vol. 50(2), pages 459-464, April.
    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. Nikolai S. Kukushkin, 2012. "On the Existence of Optima in Complete Chains and Lattices," Journal of Optimization Theory and Applications, Springer, vol. 154(3), pages 759-767, September.
    2. 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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    More about this item

    Keywords

    Binary relation; Maximal element; Necessary and sufficient condition; Potential games;
    All these keywords.

    JEL classification:

    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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