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Characterization of the existence of maximal elements of acyclic relations

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  • J.C. R. Alcantud

    ()
    (Facultad de Economía y Empresa, Universidad de Salamanca, 37008 Salamanca, SPAIN)

Abstract

We obtain a sufficient condition for the existence of maximal elements of irreflexive binary relations that generalizes the theorem of Bergstrom and Walker by relaxing the compactness condition to a weaker one that is naturally related to the relation. We then prove that the sufficient conditions used both in the Bergstrom-Walker Theorem and in our generalization provide a characterization of the existence of maximal elements of acyclic binary relations. Other sufficient conditions for the existence of maximal elements obtained by Mehta, by Peris and Subiza and by Campbell and Walker are shown to be necessary too.

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Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 19 (2002)
Issue (Month): 2 ()
Pages: 407-416

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Handle: RePEc:spr:joecth:v:19:y:2002:i:2:p:407-416

Note: Received: May 28, 1997; revised version: October 5, 2000
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Related research

Keywords: Maximal elements; Acyclicity; $\succ $-compactness.;

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Cited by:
  1. Salonen, Hannu & Vartiainen, Hannu, 2010. "On the existence of undominated elements of acyclic relations," Mathematical Social Sciences, Elsevier, vol. 60(3), pages 217-221, November.
  2. J C R Alcantud, 2004. "Maximality with or without binariness: transfer-type characterizations," Microeconomics 0402015, EconWPA.
  3. Andrikopoulos, Athanasios & Zacharias, Eleftherios, 2008. "General solutions for choice sets: The Generalized Optimal-Choice Axiom set," MPRA Paper 11645, University Library of Munich, Germany.
  4. Alcantud, José Carlos R. & Bosi, Gianni & Zuanon, Magalì, 2009. "A selection of maximal elements under non-transitive indifferences," MPRA Paper 16601, University Library of Munich, Germany.
  5. John Duggan, 2011. "General Conditions for Existence of Maximal Elements via the Uncovered Set," RCER Working Papers 563, University of Rochester - Center for Economic Research (RCER).
  6. Athanasios Andrikopoulos, 2011. "Characterization of the existence of semicontinuous weak utilities for binary relations," Theory and Decision, Springer, vol. 70(1), pages 13-26, January.

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