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A Kkm-Result And An Application For Binary And Non-Binary Choice Functions

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  • Begoña Subiza

    (Universidad de Alicante)

Abstract

By generalizing the classical Knaster-Kuratowski-Mazurkiewicz Theorem, we obtain a result that provides sufficient conditions to ensure the non-emptiness of several kinds of choice functions. This result generalizes well-known results on the existence of maximal elements for binary relations (Bergstrom, 1975; Walker, 1977; Tian, 1993), on the non-emptiness of non-binary choice functions (Nehring, 1996; Llinares and Sánchez, 1999) and on the non-emptiness of some classical solutions for tournaments (top cycle and uncovered set) on non-finite sets.

Suggested Citation

  • Begoña Subiza, 2000. "A Kkm-Result And An Application For Binary And Non-Binary Choice Functions," Working Papers. Serie AD 2000-04, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    • Handle: RePEc:ivi:wpasad:2000-04
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    References listed on IDEAS

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    2. Llinares, Juan-Vicente & Sanchez, M. Carmen, 1999. "Non-binary choice functions on non-compact sets," Economics Letters, Elsevier, vol. 63(1), pages 29-32, April.
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    5. Llinares, Juan-Vicente, 1998. "Unified treatment of the problem of existence of maximal elements in binary relations: a characterization," Journal of Mathematical Economics, Elsevier, vol. 29(3), pages 285-302, April.
    6. Guoqiang Tian, 1993. "Necessary and Sufficient Conditions for Maximization of a Class of Preference Relations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(4), pages 949-958.
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    11. 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. Alcantud, J.C.R., 2008. "Mixed choice structures, with applications to binary and non-binary optimization," Journal of Mathematical Economics, Elsevier, vol. 44(3-4), pages 242-250, February.
    2. Athanasios Andrikopoulos, 2013. "Compactness in the choice and game theories: a characterization of rationality," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(2), pages 105-110, November.

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    Keywords

    Binary Choice Function; Non-Binary Choice Function;

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