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The prenucleolus for games with restricted cooperation

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  • Katsev, Ilya
  • Yanovskaya, Elena

Abstract

A game with restricted cooperation is a triple (N,v,Ω), where N is a finite set of players, Ω⊂2N is a nonempty collection of feasible coalitions such that N∈Ω, and v:Ω→R is a characteristic function. The definition implies that if Ω=2N, then the game (N,v,Ω)=(N,v) is the classical transferable utility (TU) cooperative game.

Suggested Citation

  • Katsev, Ilya & Yanovskaya, Elena, 2013. "The prenucleolus for games with restricted cooperation," Mathematical Social Sciences, Elsevier, vol. 66(1), pages 56-65.
    • Handle: RePEc:eee:matsoc:v:66:y:2013:i:1:p:56-65
    DOI: 10.1016/j.mathsocsci.2012.12.006
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    References listed on IDEAS

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    1. Michel Grabisch & Lijue Xie, 2011. "The restricted core of games on distributive lattices: how to share benefits in a hierarchy," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 73(2), pages 189-208, April.
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    6. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Reijnierse, Hans & Potters, Jos, 1998. "The -Nucleolus of TU-Games," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 77-96, July.
    8. Gilles, Robert P & Owen, Guillermo & van den Brink, Rene, 1992. "Games with Permission Structures: The Conjunctive Approach," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(3), pages 277-293.
    9. Orshan, Gooni, 1993. "The Prenucleolus and the Reduced Game Property: Equal Treatment Replaces Anonymity," International Journal of Game Theory, Springer;Game Theory Society, vol. 22(3), pages 241-248.
    10. M. Maschler & B. Peleg & L. S. Shapley, 1979. "Geometric Properties of the Kernel, Nucleolus, and Related Solution Concepts," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 303-338, November.
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    Cited by:

    1. Anna Khmelnitskaya & Peter Sudhölter, 2013. "The prenucleolus and the prekernel for games with communication structures," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(2), pages 285-299, October.
    2. Schouten, Jop, 2022. "Cooperation, allocation and strategy in interactive decision-making," Other publications TiSEM d5d41448-8033-4f6b-8ec0-c, Tilburg University, School of Economics and Management.
    3. Khmelnitskaya, Anna B. & Sudhölter, Peter, 2011. "The prenucleolus for games with communication structures," Discussion Papers on Economics 10/2011, University of Southern Denmark, Department of Economics.
    4. 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.
    5. Schouten, Jop & Dietzenbacher, Bas & Borm, Peter, 2019. "The Nucleolus and Inheritance of Properties in Communication Situations," Other publications TiSEM bacc7f47-9b6b-4ce4-9f97-4, Tilburg University, School of Economics and Management.
    6. J. Schouten & B. Dietzenbacher & P. Borm, 2022. "The nucleolus and inheritance of properties in communication situations," Annals of Operations Research, Springer, vol. 318(2), pages 1117-1135, November.
    7. Natalia I. Naumova, 2022. "Some solutions for generalized games with restricted cooperation," Annals of Operations Research, Springer, vol. 318(2), pages 1077-1093, November.
    8. P. García-Segador & P. Miranda, 2020. "Order cones: a tool for deriving k-dimensional faces of cones of subfamilies of monotone games," Annals of Operations Research, Springer, vol. 295(1), pages 117-137, December.
    9. Encarnación Algaba & René Brink & Chris Dietz, 2018. "Network Structures with Hierarchy and Communication," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 265-282, October.
    10. Encarnación Algaba & Rene van den Brink & Chris Dietz, 2013. "Cooperative Games on Accessible Union Stable Systems," Tinbergen Institute Discussion Papers 13-207/II, Tinbergen Institute.
    11. Elena Parilina & Artem Sedakov, 2014. "Stable Bank Cooperation for Cost Reduction Problem," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 8(1), pages 7-25, August.

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