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Sufficient conditions for the existence of stable sets of cooperative games

Author

Listed:
  • Naoki Matsumoto

    (Keio University)

  • Masaki Minegishi

    (Seikei University)

Abstract

In 1944, von Neumann and Morgenstern introduced a stable set of $n$-person cooperative games in characteristic function form, with transferable utility (called TU-games for short), which is the first solution concept for cooperative games with at least three players. It is known that every $n$-person game has a stable set if $n in {3,4}$. On the other hand, Lucas constructed a 10-person TU-game which has no stable set. However, for $5 leq n leq 9$, it is not known whether every $n$-person TU-game has a stable set. In this paper, we show two sufficient conditions for an $n$-person TU-game to have a stable set for any $ngeq 5$.

Suggested Citation

  • Naoki Matsumoto & Masaki Minegishi, 2020. "Sufficient conditions for the existence of stable sets of cooperative games," Economics Bulletin, AccessEcon, vol. 40(3), pages 1958-1962.
    • Handle: RePEc:ebl:ecbull:eb-20-00394
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    References listed on IDEAS

    as
    1. Yuan Ju & Peter Borm & Pieter Ruys, 2007. "The consensus value: a new solution concept for cooperative games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(4), pages 685-703, June.
    2. Lucchetti, R. & Patrone, F. & Tijs, S.H. & Torre, A., 1987. "Continuity properties of solution concepts for cooperative games," Other publications TiSEM 6b430c63-00ee-469b-a9aa-d, Tilburg University, School of Economics and Management.
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    More about this item

    Keywords

    Cooperative game; TU-game; Stable set.;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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