On the existence of undominated elements of acyclic relations
AbstractWe 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Mathematical Social Sciences.
Volume (Year): 60 (2010)
Issue (Month): 3 (November)
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Web page: http://www.elsevier.com/locate/inca/505565
Acyclic relations Utility function Maximal elements;
Other versions of this item:
- Hannu Salonen & Hannu Vartiainen, 2005. "On the Existence of Undominated Elements of Acyclic Relations," Game Theory and Information 0503009, EconWPA.
- C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
- D8 - Microeconomics - - Information, Knowledge, and Uncertainty
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