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Dynamic stable set as a tournament solution

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  • Hannu Vartiainen
Abstract
We define a notion of dynamic (vNM) stable set for a tournament relation. Dynamic stable set satisfies (i) an external direct stability property, and (ii) an internal indirect stability property. Importantly, stability criteria are conditioned on the histories of past play, i.e. the dominance system has memory. Due to the asymmetry of the defining stability criteria, a dynamic stable set is stable both in the direct and in the indirect sense. We characterize a dynamic stable set directly in terms of the underlying tournament relation. A connection to the covering set of Dutta (J Econ Theory 44:63–80, 1988 ) is established. Using this observation, a dynamic stable set exists. We also show that a maximal implementable outcome set is a version of the ultimate uncovered set. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Hannu Vartiainen, 2015. "Dynamic stable set as a tournament solution," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(2), pages 309-327, September.
    • Handle: RePEc:spr:sochwe:v:45:y:2015:i:2:p:309-327
    DOI: 10.1007/s00355-015-0897-0
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    Cited by:

    1. Aleksei Y. Kondratev & Vladimir V. Mazalov, 2020. "Tournament solutions based on cooperative game theory," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(1), pages 119-145, March.
    2. Vicki Knoblauch, 2020. "Von Neumann–Morgenstern stable set rationalization of choice functions," Theory and Decision, Springer, vol. 89(3), pages 369-381, October.

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    More about this item

    Keywords

    C71; C72;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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