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The Kernel/Nucleolus of a Standard Tree Game


  • Granot, D
  • Maschler, M
  • Owen, G
  • Zhu, W.R.


In this paper we characterize the nucleolus (which coincides with the kernel) of a tree enterprise. We also provide a new algorithm to compute it, which sheds light on its structure. We show that in particular cases, including a chain enterprise one can compute the nucleolus in O(n) operations, where n is the number of vertices in the tree. Coauthors are M. Maschler, G. Owen, and W. R. Zhu.

Suggested Citation

  • Granot, D & Maschler, M & Owen, G & Zhu, W.R., 1996. "The Kernel/Nucleolus of a Standard Tree Game," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(2), pages 219-244.
  • Handle: RePEc:spr:jogath:v:25:y:1996:i:2:p:219-44

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    Cited by:

    1. Hougaard, Jens Leth & Tvede, Mich & Østerdal, Lars Peter, 2013. "Cost Sharing in Chains and Other Fixed Trees," Discussion Papers of Business and Economics 12/2013, University of Southern Denmark, Department of Business and Economics.
    2. Habis, Helga & Herings, P. Jean-Jacques, 2011. "Transferable utility games with uncertainty," Journal of Economic Theory, Elsevier, vol. 146(5), pages 2126-2139, September.
    3. M. Meertens & J. Potters, 2006. "The nucleolus of trees with revenues," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(2), pages 363-382, October.
    4. Csóka, Péter & Jean-Jacques Herings, P. & Kóczy, László Á. & Pintér, Miklós, 2011. "Convex and exact games with non-transferable utility," European Journal of Operational Research, Elsevier, vol. 209(1), pages 57-62, February.
    5. Jeroen Kuipers & Dries Vermeulen & Mark Voorneveld, 2010. "A generalization of the Shapley–Ichiishi result," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(4), pages 585-602, October.
    6. Helga Habis & P. Herings, 2013. "Stochastic bankruptcy games," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(4), pages 973-988, November.
    7. Habis, Helga, 2012. "Sztochasztikus csődjátékok - avagy hogyan osszunk szét egy bizonytalan méretű tortát?
      [Stochastic bankruptcy games. How can a cake of uncertain dimensions be divided?]
      ," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(12), pages 1299-1310.
    8. Balázs Sziklai & Tamás Fleiner & Tamás Solymosi, 2014. "On the Core of Directed Acyclic Graph Games," IEHAS Discussion Papers 1418, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
    9. Miquel, S. & van Velzen, S. & Hamers, H.J.M. & Norde, H.W., 2003. "Fixed Tree Games with Repeated Players," Discussion Paper 2003-87, Tilburg University, Center for Economic Research.
    10. repec:spr:compst:v:64:y:2006:i:2:p:363-382 is not listed on IDEAS
    11. Reijnierse, Hans & Potters, Jos, 1998. "The -Nucleolus of TU-Games," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 77-96, July.
    12. Márkus, Judit & Pintér, Miklós & Radványi, Anna, 2011. "The Shapley value for airport and irrigation games," MPRA Paper 30031, University Library of Munich, Germany.
    13. Jens Leth Hougaard & Mich Tvede, 2011. "Incremental Cost Sharing in Chains and Fixed Trees," MSAP Working Paper Series 02_2011, University of Copenhagen, Department of Food and Resource Economics.
    14. Kuipers, Jeroen & Mosquera, Manuel A. & Zarzuelo, José M., 2013. "Sharing costs in highways: A game theoretic approach," European Journal of Operational Research, Elsevier, vol. 228(1), pages 158-168.
    15. F.Javier Martínez-de-Albéniz & Carles Rafels & Neus Ybern, 2015. "Insights into the nucleolus of the assignment game," UB Economics Working Papers 2015/333, Universitat de Barcelona, Facultat d'Economia i Empresa, UB Economics.

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