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 paperProfessional

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

Publication series

SeriesGSBE Research Memoranda
Number017
ISSN2666-8807

JEL classifications

  • c71 - Cooperative Games

Keywords

  • coalition structure core
  • sequential dominance

Cite this

Herings, P. J-J., & Kóczy, L. Á. (2020). The Equivalence of the Minimal Dominant Set and the Myopic Stable Set for Coalition Function Form Games. Maastricht University, Graduate School of Business and Economics. GSBE Research Memoranda, No. 017 https://doi.org/10.26481/umagsb.2020017