IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v108y2018icp146-151.html
   My bibliography  Save this article

The Shapley value of conjunctive-restricted games

Author

Listed:
  • Derks, Jean

Abstract

We consider transferable utility games, where restricted cooperation is modeled by a fixed mapping assigning to each coalition the set of players that are controlled by this coalition. We study the Shapley value on the resulting class of restricted games, and provide axiomatic frameworks characterizing this value. Studies show that several classes of so-called conjunctive restrictions lead to frameworks similar to the original introduced by Shapley in 1953. We show that conjunctivity of the restriction is not only sufficient but also necessary.

Suggested Citation

  • Derks, Jean, 2018. "The Shapley value of conjunctive-restricted games," Games and Economic Behavior, Elsevier, vol. 108(C), pages 146-151.
  • Handle: RePEc:eee:gamebe:v:108:y:2018:i:c:p:146-151
    DOI: 10.1016/j.geb.2018.01.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S089982561830023X
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.geb.2018.01.012?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. Gilles, Robert P & Owen, Guillermo & van den Brink, Rene, 1992. "Games with Permission Structures: The Conjunctive Approach," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(3), pages 277-293.
    2. René Brink & Ilya Katsev & Gerard Laan, 2011. "Axiomatizations of two types of Shapley values for games on union closed systems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 47(1), pages 175-188, May.
    3. Rene van den Brink & Ilya Katsev & Gerard van der Laan, 2011. "Games on Union Closed Systems," Tinbergen Institute Discussion Papers 11-036/1, Tinbergen Institute.
    4. van den Brink, Rene & Gilles, Robert P., 1996. "Axiomatizations of the Conjunctive Permission Value for Games with Permission Structures," Games and Economic Behavior, Elsevier, vol. 12(1), pages 113-126, January.
    5. Derks, Jean & Peters, Hans, 1993. "A Shapley Value for Games with Restricted Coalitions," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(4), pages 351-360.
    6. Faigle, U & Kern, W, 1992. "The Shapley Value for Cooperative Games under Precedence Constraints," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(3), pages 249-266.
    Full references (including those not matched with items on IDEAS)

    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. René Brink & P. Herings & Gerard Laan & A. Talman, 2015. "The Average Tree permission value for games with a permission tree," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(1), pages 99-123, January.
    2. René Brink & Chris Dietz & Gerard Laan & Genjiu Xu, 2017. "Comparable characterizations of four solutions for permission tree games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(4), pages 903-923, April.
    3. Rene van den Brink & Ilya Katsev & Gerard van der Laan, 2023. "Properties of Solutions for Games on Union-Closed Systems," Mathematics, MDPI, vol. 11(4), pages 1-16, February.
    4. Encarnacion Algaba & Rene van den Brink, 2021. "Networks, Communication and Hierarchy: Applications to Cooperative Games," Tinbergen Institute Discussion Papers 21-019/IV, Tinbergen Institute.
    5. Zhengxing Zou & Qiang Zhang, 2018. "Harsanyi power solution for games with restricted cooperation," Journal of Combinatorial Optimization, Springer, vol. 35(1), pages 26-47, January.
    6. E. Algaba & J. Bilbao & R. Brink, 2015. "Harsanyi power solutions for games on union stable systems," Annals of Operations Research, Springer, vol. 225(1), pages 27-44, February.
    7. René Brink, 2017. "Games with a permission structure - A survey on generalizations and applications," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 1-33, April.
    8. Algaba, A. & Bilbao, J.M. & van den Brink, J.R. & Jiménez-Losada, A., 2000. "Cooperative Games on Antimatroids," Discussion Paper 2000-124, Tilburg University, Center for Economic Research.
    9. Béal, Sylvain & Moyouwou, Issofa & Rémila, Eric & Solal, Philippe, 2020. "Cooperative games on intersection closed systems and the Shapley value," Mathematical Social Sciences, Elsevier, vol. 104(C), pages 15-22.
    10. Encarnacion Algaba & Rene van den Brink, 2019. "The Shapley Value and Games with Hierarchies," Tinbergen Institute Discussion Papers 19-064/II, Tinbergen Institute.
    11. Algaba, A. & Bilbao, J.M. & van den Brink, J.R. & Jiménez-Losada, A., 2000. "Cooperative Games on Antimatroids," Other publications TiSEM 907b4b44-90f9-4faa-9473-8, Tilburg University, School of Economics and Management.
    12. Sylvain Béal & Issofa Moyouwou & Eric Rémila & Phillippe Solal, 2018. "Cooperative games on intersection closed systems and the Shapley value," Working Papers 2018-06, CRESE.
    13. Emilio Calvo & Esther Gutiérrez-López, 2015. "The value in games with restricted cooperation," Discussion Papers in Economic Behaviour 0115, University of Valencia, ERI-CES.
    14. Derks, Jean & Peters, Hans, 1997. "Consistent restricted Shapley values," Mathematical Social Sciences, Elsevier, vol. 33(1), pages 75-91, February.
    15. Richard Baron & Sylvain Béal & Eric Rémila & Philippe Solal, 2011. "Average tree solutions and the distribution of Harsanyi dividends," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(2), pages 331-349, May.
    16. Hougaard, Jens Leth & Moreno-Ternero, Juan D. & Tvede, Mich & Østerdal, Lars Peter, 2017. "Sharing the proceeds from a hierarchical venture," Games and Economic Behavior, Elsevier, vol. 102(C), pages 98-110.
    17. Subhadip Chakrabarti & Amandine Ghintran & Rajnish Kumar, 2019. "Assignment of heterogeneous agents in trees under the permission value," Review of Economic Design, Springer;Society for Economic Design, vol. 23(3), pages 155-188, December.
    18. René van den Brink, 2017. "Games with a Permission Structure: a survey on generalizations and applications," Tinbergen Institute Discussion Papers 17-016/II, Tinbergen Institute.
    19. E. C. Gavilán & C. Manuel & R. Brink, 2023. "Directed communication in games with directed graphs," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 584-617, October.
    20. David Lowing, 2023. "Allocation rules for multi-choice games with a permission tree structure," Annals of Operations Research, Springer, vol. 320(1), pages 261-291, January.

    More about this item

    Keywords

    Transferable utility games; Restricted cooperation; Shapley value; Axiomatic approach; Conjunctive restriction;
    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:eee:gamebe:v:108:y:2018:i:c:p:146-151. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    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.