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The nucleolus of trees with revenues

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  • M. Meertens
  • J. Potters

Abstract

Trees with revenues are a generalization of standard trees. In a tree with revenues, players have to pay for their connections to the root, but a player can also earn some revenue from being connected to the root. In this paper, we present an algorithm for calculating the nucleolus. Copyright Springer-Verlag 2006

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:64:y:2006:i:2:p:363-382
    DOI: 10.1007/s00186-006-0088-y
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    References listed on IDEAS

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    1. Nimrod Megiddo, 1978. "Computational Complexity of the Game Theory Approach to Cost Allocation for a Tree," Mathematics of Operations Research, INFORMS, vol. 3(3), pages 189-196, August.
    2. 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).
    3. S.C. Littlechild & G.F. Thompson, 1977. "Aircraft Landing Fees: A Game Theory Approach," Bell Journal of Economics, The RAND Corporation, vol. 8(1), pages 186-204, Spring.
    4. 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.
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    Cited by:

    1. Arantza Estévez-Fernández & Peter Borm & Marc Meertens & Hans Reijnierse, 2009. "On the core of routing games with revenues," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(2), pages 291-304, June.
    2. Estévez-Fernández, Arantza & Reijnierse, Hans, 2014. "On the core of cost-revenue games: Minimum cost spanning tree games with revenues," European Journal of Operational Research, Elsevier, vol. 237(2), pages 606-616.
    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. Zhang Jiangao & Shitao Yang, 2016. "On the Lexicographic Centre of Multiple Objective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 600-614, February.

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    More about this item

    Keywords

    Tree games; Revenues; Nucleolus; C71;
    All these keywords.

    JEL classification:

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

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