Maximal elements of acyclic relations on compact sets

Maximal elements for irreflexive binary relations on compact sets

The aim of this paper is to provide necessary and sufficient continuity conditions for the existence of maximal elements of irreflexive, acyclic and transitive binary relations defined on compact sets. The results answer a question raised by Campbell and Walker [Journal of Economic Theory 50 (1990) 459–464], among others, who in fact established a sufficient continuity condition for interval or...

Characterization of the existence of maximal elements of acyclic relations

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 t...

Transfer Method for Characterizing the Existence of Maximal Elements of Binary Relations on Compact or Noncompact Sets

On the existence of undominated elements of acyclic relations

We study the existence of undominated elements of acyclic relations. A sufficient condition for the existence is given without any topological assumptions when the dominance relation is finite valued. The condition says that there is a point such that all dominance sequences starting from this point are reducible. A dominance sequence is reducible, if it is possible to remove some elements from...

Maximal Elements of Weakly Continuous Relations*

A weaker than usual continuity property is defined for binary relations. Relations that have this property, along with certain transitivity properties, are shown to have maximal elements on compact sets. The results cover “interval orders,” the kind of relations that often characterize choice situations in which similar alternatives are indistinguishable. Journal of‘ Economic Literature Classif...