IDEAS home Printed from https://ideas.repec.org/a/spr/operea/v20y2020i2d10.1007_s12351-017-0341-6.html
   My bibliography  Save this article

The extended Shapley value for generalized cooperative games under precedence constraints

Author

Listed:
  • Zhengxing Zou

    (Beijing Institute of Technology)

  • Qiang Zhang

    (Beijing Institute of Technology)

  • Surajit Borkotokey

    (Dibrugarh University)

  • Xiaohui Yu

    (Beijing Wuzi University)

Abstract

We introduce a new class of games where cooperation among players is restricted by precedence constraints vis á vis the worth of a coalition depends on the order in which the players enter into the coalition. The idea combines two existing classes of cooperative games, namely the cooperative games under precedence constraints due to Faigle and Kern (Int J Game Theory 21(3):249–266, 1992) and the games in generalized characteristic function due to Nowak and Radzik (Games Econ Behav 6(1):150–161, 1994). A Shapley value for this special class of games is proposed, we call it the extended Shapley value to distinguish it for the existing one. Two axiomatic characterizations of the extended Shapley value are given: one uses Efficiency, Null player, and Linearity; the other uses Efficiency, Marginality, and Null game. Some interesting properties of the extended Shapley value are studied. Furthermore, two extensions of the extended Shapley value, called the extended probabilistic value and the extended order value, are proposed and characterized. Our study shows that the results in cooperative games under precedence constraints cannot have a trivial extension to the generalized constrained games and conversely.

Suggested Citation

  • Zhengxing Zou & Qiang Zhang & Surajit Borkotokey & Xiaohui Yu, 2020. "The extended Shapley value for generalized cooperative games under precedence constraints," Operational Research, Springer, vol. 20(2), pages 899-925, June.
    • Handle: RePEc:spr:operea:v:20:y:2020:i:2:d:10.1007_s12351-017-0341-6
    DOI: 10.1007/s12351-017-0341-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s12351-017-0341-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s12351-017-0341-6?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. van den Brink, René & González-Arangüena, Enrique & Manuel, Conrado & del Pozo, Mónica, 2014. "Order monotonic solutions for generalized characteristic functions," European Journal of Operational Research, Elsevier, vol. 238(3), pages 786-796.
    2. Jackson, Matthew O., 2005. "Allocation rules for network games," Games and Economic Behavior, Elsevier, vol. 51(1), pages 128-154, April.
    3. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    4. Nowak Andrzej S. & Radzik Tadeusz, 1994. "The Shapley Value for n-Person Games in Generalized Characteristic Function Form," Games and Economic Behavior, Elsevier, vol. 6(1), pages 150-161, January.
    5. E. Algaba & J. M. Bilbao & P. Borm & J. J. López, 2000. "The position value for union stable systems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 52(2), pages 221-236, November.
    6. Borm, P.E.M. & Owen, G. & Tijs, S.H., 1992. "On the position value for communication situations," Other publications TiSEM 5a8473e4-1df7-42df-ad53-f, Tilburg University, School of Economics and Management.
    7. 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.
    8. Calvo, Emilio & Javier Lasaga, J. & Winter, Eyal, 1996. "The principle of balanced contributions and hierarchies of cooperation," Mathematical Social Sciences, Elsevier, vol. 31(3), pages 171-182, June.
    9. 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.
    10. Meng, Fanyong & Chen, Xiaohong & Zhang, Qiang, 2015. "A coalitional value for games on convex geometries with a coalition structure," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 605-614.
    11. Bilbao, J.M. & Ordóñez, M., 2009. "Axiomatizations of the Shapley value for games on augmenting systems," European Journal of Operational Research, Elsevier, vol. 196(3), pages 1008-1014, August.
    12. J. M. Bilbao & T. S. H. Driessen & A. Jiménez Losada & E. Lebrón, 2001. "The Shapley value for games on matroids: The static model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 53(2), pages 333-348, June.
    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. Jun Su & Yuan Liang & Guangmin Wang & Genjiu Xu, 2020. "Characterizations, Potential, and an Implementation of the Shapley-Solidarity Value," Mathematics, MDPI, vol. 8(11), pages 1-20, November.
    2. C. Manuel & D. Martín, 2021. "A value for communication situations with players having different bargaining abilities," Annals of Operations Research, Springer, vol. 301(1), pages 161-182, June.

    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. C. Manuel & D. Martín, 2021. "A value for communication situations with players having different bargaining abilities," Annals of Operations Research, Springer, vol. 301(1), pages 161-182, June.
    2. 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.
    3. Michel Grabisch, 2013. "The core of games on ordered structures and graphs," Annals of Operations Research, Springer, vol. 204(1), pages 33-64, April.
    4. 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.
    5. 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.
    6. Takashi Ui & Hiroyuki Kojima & Atsushi Kajii, 2011. "The Myerson value for complete coalition structures," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(3), pages 427-443, December.
    7. Encarnaciön Algaba & Sylvain Béal & Eric Rémila & Phillippe Solal, 2018. "Harsanyi power solutions for cooperative games on voting structures," Working Papers 2018-05, CRESE.
    8. Encarnacion Algaba & Rene van den Brink, 2019. "The Shapley Value and Games with Hierarchies," Tinbergen Institute Discussion Papers 19-064/II, Tinbergen Institute.
    9. Encarnacion Algaba & Rene van den Brink, 2021. "Networks, Communication and Hierarchy: Applications to Cooperative Games," Tinbergen Institute Discussion Papers 21-019/IV, Tinbergen Institute.
    10. Encarnación Algaba & René Brink & Chris Dietz, 2017. "Power Measures and Solutions for Games Under Precedence Constraints," Journal of Optimization Theory and Applications, Springer, vol. 172(3), pages 1008-1022, March.
    11. Conrado M. Manuel & Daniel Martín, 2020. "A Monotonic Weighted Shapley Value," Group Decision and Negotiation, Springer, vol. 29(4), pages 627-654, August.
    12. Emilio Calvo & Esther Gutiérrez-López, 2015. "The value in games with restricted cooperation," Discussion Papers in Economic Behaviour 0115, University of Valencia, ERI-CES.
    13. 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.
    14. Herings, P. Jean-Jacques & van der Laan, Gerard & Talman, Dolf, 2007. "The socially stable core in structured transferable utility games," Games and Economic Behavior, Elsevier, vol. 59(1), pages 85-104, April.
    15. 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.
    16. van den Brink, René & González-Arangüena, Enrique & Manuel, Conrado & del Pozo, Mónica, 2014. "Order monotonic solutions for generalized characteristic functions," European Journal of Operational Research, Elsevier, vol. 238(3), pages 786-796.
    17. Meng, Fanyong & Chen, Xiaohong & Zhang, Qiang, 2015. "A coalitional value for games on convex geometries with a coalition structure," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 605-614.
    18. 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.
    19. Enrique González-Arangüena & Conrado Manuel & Daniel Gomez & René van den Brink, 2008. "A Value for Directed Communication Situations," Tinbergen Institute Discussion Papers 08-006/1, Tinbergen Institute.
    20. Bilbao, J.M. & Ordóñez, M., 2009. "Axiomatizations of the Shapley value for games on augmenting systems," European Journal of Operational Research, Elsevier, vol. 196(3), pages 1008-1014, August.

    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:operea:v:20:y:2020:i:2:d:10.1007_s12351-017-0341-6. 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.