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On the existence of undominated elements of acyclic relations

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  • Salonen, Hannu
  • Vartiainen, Hannu

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.

Suggested Citation

  • Salonen, Hannu & Vartiainen, Hannu, 2010. "On the existence of undominated elements of acyclic relations," Mathematical Social Sciences, Elsevier, vol. 60(3), pages 217-221, November.
    • Handle: RePEc:eee:matsoc:v:60:y:2010:i:3:p:217-221
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    1. J.C. R. Alcantud, 2002. "Characterization of the existence of maximal elements of acyclic relations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(2), pages 407-416.
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    Cited by:

    1. Hannu Salonen & Hannu Vartiainen, 2011. "On the Existence of Markov Perfect Equilibria in Perfect Information Games," Discussion Papers 68, Aboa Centre for Economics.
    2. Hannu Salonen, 2013. "Utilitarian Preferences and Potential Games," Discussion Papers 85, Aboa Centre for Economics.

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    More about this item

    Keywords

    Acyclic relations Utility function Maximal elements;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

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