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The core and the steady bargaining set for convex games

Author

Listed:
  • Josep Maria Izquierdo

    (Universitat de Barcelona)

  • Carles Rafels

    (Universitat de Barcelona)

Abstract

Within the class of zero-monotonic and grand coalition superadditive cooperative games with transferable utility, the convexity of a game is characterized by the coincidence of its core and the steady bargaining set. As a consequence it is proved that convexity can also be characterized by the coincidence of the core of a game and the modified Zhou bargaining set à la Shimomura.

Suggested Citation

  • Josep Maria Izquierdo & Carles Rafels, 2018. "The core and the steady bargaining set for convex games," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(1), pages 35-54, March.
    • Handle: RePEc:spr:jogath:v:47:y:2018:i:1:d:10.1007_s00182-017-0576-8
    DOI: 10.1007/s00182-017-0576-8
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    References listed on IDEAS

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    1. Marina Núñez & Carles Rafels, 1998. "On extreme points of the core and reduced games," Annals of Operations Research, Springer, vol. 84(0), pages 121-133, December.
    2. Tamás Solymosi, 2008. "Bargaining sets and the core in partitioning games," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 16(4), pages 425-440, December.
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    8. Einy, Ezra & Wettstein, David, 1996. "Equivalence between Bargaining Sets and the Core in Simple Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(1), pages 65-71.
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    Cited by:

    1. Elena Iñarra & Roberto Serrano & Ken-Ichi Shimomura, 2020. "The Nucleolus, the Kernel, and the Bargaining Set: An Update," Revue économique, Presses de Sciences-Po, vol. 71(2), pages 225-266.

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