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Maximality with or without binariness: transfer-type characterizations

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Author Info
J C R Alcantud

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Abstract

We provide the first necessary and su±cient conditions in the literature for the existence of maximal elements in a non-binary choice framework. As an application, the characterization of the existence of maximal elements for acyclic binary relations obtained in Rodriguez-Palmero and Garcia-Lapresta, 2002, Mathematical Social Sciences 43, 55-60, is deduced as a Corollary. Further characterizations in di®erent settings given by Tian and Zhou, 1995, Journal of Mathematical Economics 24, 281- 303, follow as well. Analogous characterization problems in the k- acyclic binary cases are solved too.

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Paper provided by EconWPA in its series Microeconomics with number 0402015.

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Length: 10 pages
Date of creation: 28 Feb 2004
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Handle: RePEc:wpa:wuwpmi:0402015

Note: Type of Document - PDF; prepared on WinXP; pages: 10
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Related research
Keywords: maximization; non-binary choice function; transfer-continuity; k-acyclicity;

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Find related papers by JEL classification:
D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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  1. 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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  2. J. C. R. Alcantud & Carlos Alós-Ferrer, 2002. "Choice-Nash Equilibria," Vienna Economics Papers 0209, University of Vienna, Department of Economics. [Downloadable!]
  3. Rodriguez-Palmero, Carlos & Garcia-Lapresta, Jose-Luis, 2002. "Maximal elements for irreflexive binary relations on compact sets," Mathematical Social Sciences, Elsevier, vol. 43(1), pages 55-60, January. [Downloadable!] (restricted)
  4. Alcantud, J. C. R., 2002. "Non-binary choice in a non-deterministic model," Economics Letters, Elsevier, vol. 77(1), pages 117-123, September. [Downloadable!] (restricted)
  5. 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)
  6. 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)
  7. Klaus Nehring, 1997. "Rational choice and revealed preference without binariness," Social Choice and Welfare, Springer, vol. 14(3), pages 403-425. [Downloadable!] (restricted)
  8. Tian, Guoqiang & Zhou, Jianxin, 1995. "Transfer continuities, generalizations of the Weierstrass and maximum theorems: A full characterization," Journal of Mathematical Economics, Elsevier, vol. 24(3), pages 281-303. [Downloadable!] (restricted)
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