Characterization of the existence of maximal elements of acyclic relations
AbstractWe 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 InfoArticle provided by Springer in its journal Economic Theory.
Volume (Year): 19 (2002)
Issue (Month): 2 ()
Note: Received: May 28, 1997; revised version: October 5, 2000
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- Salonen, Hannu & Vartiainen, Hannu, 2010.
"On the existence of undominated elements of acyclic relations,"
Mathematical Social Sciences,
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- Hannu Salonen & Hannu Vartiainen, 2005. "On the Existence of Undominated Elements of Acyclic Relations," Game Theory and Information 0503009, EconWPA.
- J C R Alcantud, 2004.
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- Alcantud, Jose C.R., 2006. "Maximality with or without binariness: Transfer-type characterizations," Mathematical Social Sciences, Elsevier, vol. 51(2), pages 182-191, March.
- Andrikopoulos, Athanasios & Zacharias, Eleftherios, 2008. "General solutions for choice sets: The Generalized Optimal-Choice Axiom set," MPRA Paper 11645, University Library of Munich, Germany.
- 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.
- 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).
- 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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