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Weighted allocation rules for standard fixed tree games

Author

Listed:
  • Endre Bjørndal
  • Maurice Koster
  • Stef Tijs

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

Suggested Citation

  • Endre Bjørndal & Maurice Koster & Stef Tijs, 2004. "Weighted allocation rules for standard fixed tree games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(2), pages 249-270, June.
    • Handle: RePEc:spr:mathme:v:59:y:2004:i:2:p:249-270
    DOI: 10.1007/s001860300324
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. repec:zbw:rwirep:0212 is not listed on IDEAS

    More about this item

    Keywords

    Cooperative games; 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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