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The bargaining set of four-person balanced games

Author

Listed:
  • Tamás Solymosi

    (Department of Operations Research, Budapest University of Economic Sciences and Public Administration, 1828 Budapest, Pf. 489, Hungary, phone: +36-1-456 6757, fax: +36-1-456 6435, e-mail: tamas.solymosi@opkut.bke.hu)

Abstract

It is well known that in three-person transferable-utility cooperative games the bargaining set {\cal M}i1 and the core coincide for any coalition structure, provided the latter solution is not empty. In contrast, five-person totally-balanced games are discussed in the literature in which the bargaining set {\cal M}i1 (for the grand coalition) is larger then the core. This paper answers the equivalence question in the remaining four-person case. We prove that in any four-person game and for arbitrary coalition structure, whenever the core is not empty, it coincides with the bargaining set {\cal M}i1. Our discussion employs a generalization of balancedness to games with coalition structures.

Suggested Citation

  • Tamás Solymosi, 2002. "The bargaining set of four-person balanced games," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(1), pages 1-11.
    • Handle: RePEc:spr:jogath:v:31:y:2002:i:1:p:1-11
    Note: Received: August 2001/Revised version: April 2002
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    Citations

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    Cited by:

    1. Atay, Ata & Solymosi, Tamás, 2018. "On bargaining sets of supplier-firm-buyer games," Economics Letters, Elsevier, vol. 167(C), pages 99-103.
    2. 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.
    3. Michel Le Breton & Karine Van Der Straeten, 2017. "Alliances Électorales et Gouvernementales : La Contribution de la Théorie des Jeux Coopératifs à la Science Politique," Revue d'économie politique, Dalloz, vol. 127(4), pages 637-736.
    4. Hugues Tchantcho & Issofa Moyouwou & Nicolas G. Andjiga, 2012. "On the bargaining set of three-player games," Economics Bulletin, AccessEcon, vol. 32(1), pages 429-436.
    5. Tamás Solymosi, 2015. "The kernel is in the least core for permutation 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. 23(4), pages 795-809, December.

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