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Weighted Allocation Rules for Standard Fixed Tree Games

Author

Listed:
  • Bjorndal, E.
  • Koster, M.A.L.

    (Tilburg University, Center For Economic Research)

  • Tijs, S.H.

    (Tilburg University, Center For Economic Research)

Abstract

In this paper we consider standard fixed tree games, for which each vertex unequal to the root is inhabited by exactly one player. We present two weighted allocation rules, the weighted down-home allocation and the weighted neighbour-home allocation, both inspired by the painting story in Maschler et al. (1995) . We show, in a constructive way, that the core equals both the set of weighted down-home allocations and the set of weighted neighbour allocations. Since every weighted down-home allocation specifies a weighted Shapley value (Kalai and Samet (1988)) in a natural way, and vice versa, our results provide an alternative proof of the fact that the core of a standard fixed tree game equals the set of weighted Shapley values. The class of weighted neighbour allocations is a generalization of the nucleolus, in the sense that the latter is in this class as the special member where players have all equal weights. Copyright Springer-Verlag 2004
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Suggested Citation

  • Bjorndal, E. & Koster, M.A.L. & Tijs, S.H., 1999. "Weighted Allocation Rules for Standard Fixed Tree Games," Discussion Paper 1999-79, Tilburg University, Center for Economic Research.
    • Handle: RePEc:tiu:tiucen:1f5f0df4-3b22-419d-92ca-7f3ab8ffc1d2
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    File URL: https://pure.uvt.nl/ws/portalfiles/portal/532660/79.pdf
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    Cited by:

    1. Panova, Elena, 2023. "Sharing cost of network among users with differentiated willingness to pay," Games and Economic Behavior, Elsevier, vol. 142(C), pages 666-689.
    2. Stefano Moretti & Henk Norde, 2022. "Some new results on generalized additive games," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(1), pages 87-118, March.
    3. repec:zbw:rwirep:0212 is not listed on IDEAS
    4. von Schnurbein, Barbara, 2010. "The Core of an Extended Tree Game: A New Characterisation," Ruhr Economic Papers 212, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    5. Barbara von Schnurbein, 2010. "The Core of an Extended Tree Game: A New Characterisation," Ruhr Economic Papers 0212, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.

    More about this item

    Keywords

    cooperative game theory; tree games; core; weighted Shapley value; nucleolus;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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