Characterization of the existence of maximal elements of acyclic relations

José Alcantud ()

Economic Theory, 2002, vol. 19, issue 2, 407-416

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.

Keywords: Maximal elements; Acyclicity; $\succ $-compactness. (search for similar items in EconPapers)
JEL-codes: D11 (search for similar items in EconPapers)
Date: 2001-10-29
Note: Received: May 28, 1997; revised version: October 5, 2000
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Citations: View citations in EconPapers (12)

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