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

P. Jean-Jacques Herings and László Kóczy ()

No 17, Research Memorandum from Maastricht University, Graduate School of Business and Economics (GSBE)

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.

JEL-codes: C71 (search for similar items in EconPapers)
Date: 2020-06-09
New Economics Papers: this item is included in nep-des, nep-gth and nep-ore
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Related works:
Journal Article: The equivalence of the minimal dominant set and the myopic stable set for coalition function form games (2021)
Working Paper: The Equivalence of the Minimal Dominant Set and the Myopic Stable Set for Coalition Function Form Games (2020)
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Persistent link: https://EconPapers.repec.org/RePEc:unm:umagsb:2020017

DOI: 10.26481/umagsb.2020017

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