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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

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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 [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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Publisher 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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  1. 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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  2. 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)
  3. 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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  4. 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).
  5. Kim, Taesung & Richter, Marcel K., 1986. "Nontransitive-nontotal consumer theory," Journal of Economic Theory, Elsevier, vol. 38(2), pages 324-363, April. [Downloadable!] (restricted)
  6. 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)
  7. 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)
  8. Klaus Nehring, 1997. "Rational choice and revealed preference without binariness," Social Choice and Welfare, Springer, vol. 14(3), pages 403-425. [Downloadable!] (restricted)
  9. 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)
  10. 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)
  11. 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)
  12. Walker, Mark, 1977. "On the existence of maximal elements," Journal of Economic Theory, Elsevier, vol. 16(2), pages 470-474, December. [Downloadable!] (restricted)
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