The Equivalence of the Minimal Dominant Set and the Myopic Stable Set for Coalition Function Form Games

P. Jean-Jacques Herings, László Á. Kóczy

Research output: Working paper / PreprintWorking paper

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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.
Original languageEnglish
PublisherMaastricht University, Graduate School of Business and Economics
Number of pages24
Publication statusPublished - 9 Jun 2020

Publication series

SeriesGSBE Research Memoranda

JEL classifications

  • c71 - Cooperative Games


  • coalition structure core
  • sequential dominance

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