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

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Author Info
Begoña Subiza () (Universidad de Alicante)

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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
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Publisher 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
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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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  1. Nehring, Klaus, 1996. "Maximal elements of non-binary choice functions on compact sets," Economics Letters, Elsevier, vol. 50(3), pages 337-340, March. [Downloadable!] (restricted)
  2. Ted Bergstrom, 1975. "Maximal elements of Acyclic Relations on Compact Sets," University of California at Santa Barbara, Economics Working Paper Series 1975B, Department of Economics, UC Santa Barbara. [Downloadable!]
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  3. Tian, Guoqiang, 1993. "Necessary and Sufficient Conditions for Maximization of a Class of Preference Relations," Review of Economic Studies, Blackwell Publishing, vol. 60(4), pages 949-58, October. [Downloadable!] (restricted)
  4. Klaus Nehring, 1997. "Rational choice and revealed preference without binariness," Social Choice and Welfare, Springer, vol. 14(3), pages 403-425. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
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  6. 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).
  7. 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. [Downloadable!] (restricted)
  8. 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. [Downloadable!] (restricted)
  9. Kim, Taesung & Richter, Marcel K., 1986. "Nontransitive-nontotal consumer theory," Journal of Economic Theory, Elsevier, vol. 38(2), pages 324-363, April. [Downloadable!] (restricted)
  10. Campbell, Donald E. & Walker, Mark, 1990. "Maximal elements of weakly continuous relations," Journal of Economic Theory, Elsevier, vol. 50(2), pages 459-464, April. [Downloadable!] (restricted)
  11. Walker, Mark, 1977. "On the existence of maximal elements," Journal of Economic Theory, Elsevier, vol. 16(2), pages 470-474, December. [Downloadable!] (restricted)
  12. 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. [Downloadable!] (restricted)
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