IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v64y2006i2p363-382.html
   My bibliography  Save this article

The nucleolus of trees with revenues

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00186-006-0088-y
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00186-006-0088-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Daniel Granot & Jeroen Kuipers & Sunil Chopra, 2002. "Cost Allocation for a Tree Network with Heterogeneous Customers," Mathematics of Operations Research, INFORMS, vol. 27(4), pages 647-661, November.
    3. Elena Iñarra & Roberto Serrano & Ken-Ichi Shimomura, 2020. "The Nucleolus, the Kernel, and the Bargaining Set: An Update," Revue économique, Presses de Sciences-Po, vol. 71(2), pages 225-266.
    4. Peter Borm & Herbert Hamers & Ruud Hendrickx, 2001. "Operations research games: A survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(2), pages 139-199, December.
    5. 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.
    6. Xiaotie Deng & Qizhi Fang & Xiaoxun Sun, 2009. "Finding nucleolus of flow game," Journal of Combinatorial Optimization, Springer, vol. 18(1), pages 64-86, July.
    7. Sanjith Gopalakrishnan & Daniel Granot & Frieda Granot, 2021. "Consistent Allocation of Emission Responsibility in Fossil Fuel Supply Chains," Management Science, INFORMS, vol. 67(12), pages 7637-7668, December.
    8. Miquel, S. & van Velzen, S. & Hamers, H.J.M. & Norde, H.W., 2003. "Fixed Tree Games with Repeated Players," Other publications TiSEM 55d10eab-2d36-406b-8e15-4, Tilburg University, School of Economics and Management.
    9. Márkus, Judit & Pintér, Miklós & Radványi, Anna, 2011. "The Shapley value for airport and irrigation games," MPRA Paper 30031, University Library of Munich, Germany.
    10. Walter Kern & Daniël Paulusma, 2003. "Matching Games: The Least Core and the Nucleolus," Mathematics of Operations Research, INFORMS, vol. 28(2), pages 294-308, May.
    11. Csóka, Péter & Illés, Ferenc & Solymosi, Tamás, 2022. "On the Shapley value of liability games," European Journal of Operational Research, Elsevier, vol. 300(1), pages 378-386.
    12. Lech Kruś, 2009. "Cost allocation in partition function form games," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 19(2), pages 39-49.
    13. R. Brânzei & E. Iñarra & S. Tijs & J. M. Zarzuelo, 2005. "Cooperation by Asymmetric Agents in a Joint Project," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 7(4), pages 623-640, October.
    14. Tijs, S.H. & Brânzei, R., 2004. "Cases in Cooperation and Cutting the Cake," Other publications TiSEM f9573808-10b5-4a9e-a835-2, Tilburg University, School of Economics and Management.
    15. Cano-Berlanga, Sebastián & Giménez-Gómez, José-Manuel & Vilella, Cori, 2017. "Enjoying cooperative games: The R package GameTheory," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 381-393.
    16. Sexton, Richard J., 1991. "Game Theory: A Review With Applications To Vertical Control In Agricultural Markets," Working Papers 225865, University of California, Davis, Department of Agricultural and Resource Economics.
    17. Tamás Solymosi, 2019. "Weighted nucleoli and dually essential coalitions (extended version)," CERS-IE WORKING PAPERS 1914, Institute of Economics, Centre for Economic and Regional Studies.
    18. M. Fiestras-Janeiro & Ignacio García-Jurado & Manuel Mosquera, 2011. "Cooperative games and cost allocation problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 1-22, July.
    19. Endre Bjørndal & Herbert Hamers & Maurice Koster, 2004. "Cost allocation in a bank ATM network," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(3), pages 405-418, July.
    20. Sudhölter, Peter & Zarzuelo, José M., 2017. "Characterizations of highway toll pricing methods," European Journal of Operational Research, Elsevier, vol. 260(1), pages 161-170.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:mathme:v:64:y:2006:i:2:p:363-382. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.