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A KKM-result and an application for binary and non-binary choice functions

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Author Info

  • M. Carmen Sánchez
  • Juan-Vicente Llinares
  • Begoña Subiza

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 [4]; Walker [16]; Tian [15]), on the non-emptiness of non-binary choice functions (Nehring [12]; Llinares and Sánchez [9]) and on the non-emptiness of some classical solutions for tournaments (top cycle and uncovered set) on non-finite sets. Copyright Springer-Verlag Berlin Heidelberg 2003

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File URL: http://hdl.handle.net/10.1007/s00199-001-0242-y
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Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 21 (2003)
Issue (Month): 1 (01)
Pages: 185-193

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Handle: RePEc:spr:joecth:v:21:y:2003:i:1:p:185-193

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Related research

Keywords: Keywords and Phrases: KKM theorem; Non-empty choice; Non-binary choice function; Maximal elements; Tournaments.; JEL Classification Numbers: C60; D11; D71.;

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References

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  1. 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).
  2. 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).
  3. 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.
  4. 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.
  5. 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.
  6. Walker, Mark, 1977. "On the existence of maximal elements," Journal of Economic Theory, Elsevier, vol. 16(2), pages 470-474, December.
  7. Wayne Shafer & Hugo Sonnenschein, 1974. "Equilibrium in Abstract Economies Without Ordered Preferences," Discussion Papers 94, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. 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.
  9. Campbell, Donald E. & Walker, Mark, 1990. "Maximal elements of weakly continuous relations," Journal of Economic Theory, Elsevier, vol. 50(2), pages 459-464, April.
  10. Klaus Nehring, 1997. "Rational choice and revealed preference without binariness," Social Choice and Welfare, Springer, vol. 14(3), pages 403-425.
  11. Nehring, Klaus, 1996. "Maximal elements of non-binary choice functions on compact sets," Economics Letters, Elsevier, vol. 50(3), pages 337-340, March.
  12. Bergstrom, Theodore C., 1975. "Maximal elements of acyclic relations on compact sets," Journal of Economic Theory, Elsevier, vol. 10(3), pages 403-404, June.
  13. Kim, Taesung & Richter, Marcel K., 1986. "Nontransitive-nontotal consumer theory," Journal of Economic Theory, Elsevier, vol. 38(2), pages 324-363, April.
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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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