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 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.
Year of publication: |
2010
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Authors: | Salonen, Hannu ; Vartiainen, Hannu |
Published in: |
Mathematical Social Sciences. - Elsevier, ISSN 0165-4896. - Vol. 60.2010, 3, p. 217-221
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Publisher: |
Elsevier |
Keywords: | Acyclic relations Utility function Maximal elements |
Saved in:
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