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

Author

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  • P. Jean-Jacques Herings

    (Department of Economics, Maastricht University, P.O. Box 616, 6200 MD, Maastricht, The Netherlands.)

  • László Á. Kóczy

    (Institute of Economics, Centre for Economic and Regional Studies, Tóth Kálmán u. 4., 1097 Budapest, Hungary And Department of Finance, Faculty of Economics and Social Sciences, Budapest University of Technology and Economics, Magyar tudósok körútja 2, 1117 Budapest, Hungary)

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.

Suggested Citation

  • P. Jean-Jacques Herings & László Á. Kóczy, 2020. "The Equivalence of the Minimal Dominant Set and the Myopic Stable Set for Coalition Function Form Games," CERS-IE WORKING PAPERS 2022, Institute of Economics, Centre for Economic and Regional Studies.
    • Handle: RePEc:has:discpr:2022
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    References listed on IDEAS

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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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