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The equivalence of the minimal dominant set and the myopic stable set for coalition function form games

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  • Herings, P. Jean-Jacques
  • Kóczy, László Á.

Abstract

In cooperative games, the coalition structure core is, despite its potential emptiness, one of the most popular solutions. While it is a fundamentally static concept, the consideration of a sequential extension of the underlying dominance correspondence gave rise to a selection of non-empty generalizations. Among these, the payoff-equivalence minimal dominant set and the myopic stable set are defined by a similar set of conditions. We identify some problems with the payoff-equivalence minimal dominant set and propose an appropriate reformulation called the minimal dominant set. We show that replacing asymptotic external stability by sequential weak dominance leaves the myopic stable set unaffected. The myopic stable set is therefore equivalent to the minimal dominant set.

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  • Herings, P. Jean-Jacques & Kóczy, László Á., 2021. "The equivalence of the minimal dominant set and the myopic stable set for coalition function form games," Games and Economic Behavior, Elsevier, vol. 127(C), pages 67-79.
    • Handle: RePEc:eee:gamebe:v:127:y:2021:i:c:p:67-79
    DOI: 10.1016/j.geb.2021.02.003
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    Cited by:

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    More about this item

    Keywords

    Coalition structure core; Sequential dominance;

    JEL classification:

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

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