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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.

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File URL: http://www.ivie.es/downloads/docs/wpasad/wpasad-2000-04.pdf
File Function: Fisrt version / Primera version, 2000
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Bibliographic Info

Paper provided by Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) in its series Working Papers. Serie AD with number 2000-04.

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Length: 14 pages
Date of creation: Feb 2000
Date of revision:
Publication status: Published by Ivie
Handle: RePEc:ivi:wpasad:2000-04

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Keywords: Binary Choice Function; Non-Binary Choice Function;

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References

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  1. Nehring, Klaus, 1996. "Maximal elements of non-binary choice functions on compact sets," Economics Letters, Elsevier, vol. 50(3), pages 337-340, March.
  2. Walker, Mark, 1977. "On the existence of maximal elements," Journal of Economic Theory, Elsevier, vol. 16(2), pages 470-474, December.
  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. Juan Vicente Llinares Císcar, 1995. "Unified Treatment Of The Problem Of Existence Of Maximal Elements In Binary Relations. A Characterization," Working Papers. Serie AD 1995-17, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  5. Shafer, Wayne & Sonnenschein, Hugo, 1975. "Equilibrium in abstract economies without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 345-348, December.
  6. Moulin, Herve, 1994. "Social choice," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 31, pages 1091-1125 Elsevier.
  7. Klaus Nehring, 1997. "Rational choice and revealed preference without binariness," Social Choice and Welfare, Springer, vol. 14(3), pages 403-425.
  8. Kim, Taesung & Richter, Marcel K., 1986. "Nontransitive-nontotal consumer theory," Journal of Economic Theory, Elsevier, vol. 38(2), pages 324-363, April.
  9. 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.
  10. Bergstrom, Theodore C., 1975. "Maximal elements of acyclic relations on compact sets," Journal of Economic Theory, Elsevier, vol. 10(3), pages 403-404, June.
  11. Ben-El-Mechaiekh, H. & Chebbi, S. & Florenzano, M. & Llinares, J.-V., 1997. "Abstract Convexity and Fixed Points," Papiers d'Economie Mathématique et Applications 97.87, Université Panthéon-Sorbonne (Paris 1).
  12. Tian, Guoqiang & Zhou, Jianxin, 1992. "Transfer Method for Characterizing the Existence of Maximal Elements of Binary Relations on Compact or Noncompact Sets," MPRA Paper 41227, University Library of Munich, Germany.
  13. Tian, Guoqiang, 1993. "Necessary and Sufficient Conditions for Maximization of a Class of Preference Relations," Review of Economic Studies, Wiley Blackwell, vol. 60(4), pages 949-58, October.
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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.

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