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The Kernel/Nucleolus of a Standard Tree Game

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  • Granot, D, et al
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    Abstract

    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.

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    Bibliographic Info

    Article provided by Springer in its journal International Journal of Game Theory.

    Volume (Year): 25 (1996)
    Issue (Month): 2 ()
    Pages: 219-44

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    Handle: RePEc:spr:jogath:v:25:y:1996:i:2:p:219-44

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    Web page: http://link.springer.de/link/service/journals/00182/index.htm

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    Cited by:
    1. 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.
    2. Péter Csóka & P. Jean-Jacques Herings & László Á. Kóczy & Miklós Pintér, 2009. "Convex and Exact Games with Non-transferable Utility," Working Paper Series 0904, Óbuda University, Keleti Faculty of Business and Management.
    3. Kuipers, Jeroen & Vermeulen, Dries & Voorneveld, Mark, 2009. "A generalization of the Shapley-Ichiishi result," Working Paper Series in Economics and Finance 711, Stockholm School of Economics.
    4. Helga Habis & P. Herings, 2013. "Stochastic bankruptcy games," International Journal of Game Theory, Springer, vol. 42(4), pages 973-988, November.
    5. Judit Markus & Anna Radvanyi & Miklos Pinter, 2012. "The Shapley Value for Airport and Irrigation Games," IEHAS Discussion Papers 1207, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
    6. 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.
    7. Helga Habis & P. Jean-Jacques Herings, 2011. "Transferable Utility Games with Uncertainty," IEHAS Discussion Papers 1120, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
    8. 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, Department of Business and Economics, University of Southern Denmark.
    9. Koster, M.A.L. & Molina, E. & Sprumont, Y. & Tijs, S.H., 1998. "Core Representations of the Standard Fixed Tree Game," Discussion Paper 1998-21, Tilburg University, Center for Economic Research.
    10. Kuipers, J. & Feltkamp, V. & Tijs, S.H., 1996. "Vertix Weighted Steiner Tree Games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-73363, Tilburg University.
    11. 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.
    12. M. Meertens & J. Potters, 2006. "The nucleolus of trees with revenues," Computational Statistics, Springer, vol. 64(2), pages 363-382, October.

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