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...
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| Veröffentlicht in: | Mathematical social sciences 2010-11, Vol.60 (3), p.217-221 |
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| container_title | Mathematical social sciences |
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| creator | Salonen, Hannu Vartiainen, Hannu |
| description | 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. |
| doi_str_mv | 10.1016/j.mathsocsci.2010.07.003 |
| format | Article |
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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. 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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.</abstract><pub>Elsevier B.V</pub><doi>10.1016/j.mathsocsci.2010.07.003</doi><tpages>5</tpages></addata></record> |
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| ispartof | Mathematical social sciences, 2010-11, Vol.60 (3), p.217-221 |
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| language | eng |
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| source | RePEc; Elsevier ScienceDirect Journals |
| subjects | Acyclic relations Acyclic relations Utility function Maximal elements Domination Maximal elements Spatial analysis Topology Utility function Utility functions |
| title | On the existence of undominated elements of acyclic relations |
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