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