On the existence of undominated elements of acyclic relations

Hannu Salonen and Hannu Vartiainen ()

Mathematical Social Sciences, 2010, vol. 60, issue 3, 217-221

Abstract: 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 it so that the resulting subsequence is still a dominance sequence. Necessary and sufficient conditions are formulated for closed acyclic relations on compact Hausdorff spaces. Reducibility is the key concept also in this case. A representation theorem for such relations is given.

Keywords: Acyclic; relations; Utility; function; Maximal; elements (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (2)

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Related works:
Working Paper: On the Existence of Undominated Elements of Acyclic Relations (2005)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matsoc:v:60:y:2010:i:3:p:217-221

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