IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v356y2019icp190-197.html
   My bibliography  Save this article

The position value and the structures of graphs

Author

Listed:
  • Li, Daniel Li
  • Shan, Erfang

Abstract

The position value is an allocation rule based on the Shapley value of the link game from the original communication situation, in which cooperation is restricted by a graph. In the link games, feasible coalitions are connected but their structures are ignored. We introduce structure functions to describe the structures of connected sets, and generalize the link game and the position value to the setting with local structures. We modify an axiomatic characterization for the position value by Slikker to the generalized position value by component efficiency and Balanced link contributions on local structures.

Suggested Citation

  • Li, Daniel Li & Shan, Erfang, 2019. "The position value and the structures of graphs," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 190-197.
    • Handle: RePEc:eee:apmaco:v:356:y:2019:i:c:p:190-197
    DOI: 10.1016/j.amc.2019.03.041
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319302486
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.03.041?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. Marco Slikker, 2005. "A characterization of the position value," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(4), pages 505-514, November.
    2. 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.
    3. 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.
    4. Jackson, Matthew O. & Wolinsky, Asher, 1996. "A Strategic Model of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 71(1), pages 44-74, October.
    5. Takumi Kongo, 2010. "Difference between the position value and the Myerson value is due to the existence of coalition structures," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(4), pages 669-675, October.
    6. Yoshio Kamijo & Takumi Kongo, 2010. "Axiomatization of the Shapley value using the balanced cycle contributions property," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(4), pages 563-571, October.
    7. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    8. Daniel Gómez & Enrique Gonz{'a}lez-Arangüena & Conrado Manuel & Guillermo Owen & Monica Del Pozo, 2004. "A Unified Approach To The Myerson Value And The Position Value," Theory and Decision, Springer, vol. 56(2_2), pages 63-76, February.
    9. van den Nouweland, Anne & Slikker, Marco, 2012. "An axiomatic characterization of the position value for network situations," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 266-271.
    10. André Casajus, 2007. "The position value is the Myerson value, in a sense," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(1), pages 47-55, September.
    11. Daniel Gómez & Enrique Gonz{’a}lez-Arangüena & Conrado Manuel & Guillermo Owen & Monica Del Pozo, 2004. "A Unified Approach To The Myerson Value And The Position Value," Theory and Decision, Springer, vol. 56(1), pages 63-76, April.
    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. C. Manuel & E. Ortega & M. del Pozo, 2023. "Marginality and the position value," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 459-474, July.
    2. Erfang Shan & Guang Zhang & Xiaokang Shan, 2018. "The degree value for games with communication structure," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(3), pages 857-871, September.
    3. Kamijo, Yoshio, 2009. "A linear proportional effort allocation rule," Mathematical Social Sciences, Elsevier, vol. 58(3), pages 341-353, November.
    4. Surajit Borkotokey & Sujata Goala & Niharika Kakoty & Parishmita Boruah, 2022. "The component-wise egalitarian Myerson value for Network Games," Papers 2201.02793, arXiv.org.
    5. Borkotokey, Surajit & Chakrabarti, Subhadip & Gilles, Robert P. & Gogoi, Loyimee & Kumar, Rajnish, 2021. "Probabilistic network values," Mathematical Social Sciences, Elsevier, vol. 113(C), pages 169-180.
    6. René Brink & Gerard Laan & Vitaly Pruzhansky, 2011. "Harsanyi power solutions for graph-restricted games," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(1), pages 87-110, February.
    7. Napel, Stefan & Nohn, Andreas & Alonso-Meijide, José Maria, 2012. "Monotonicity of power in weighted voting games with restricted communication," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 247-257.
    8. Niharika Kakoty & Surajit Borkotokey & Rajnish Kumar & Abhijit Bora, 2024. "Weighted Myerson value for Network games," Papers 2402.11464, arXiv.org.
    9. Jean-François Caulier & Michel Grabisch & Agnieszka Rusinowska, 2015. "An allocation rule for dynamic random network formation processes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(2), pages 283-313, October.
    10. Belau, Julia, 2016. "Outside option values for network games," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 76-86.
    11. Julia Belau, 2018. "The class of ASN-position values," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(1), pages 65-99, January.
    12. André Casajus, 2007. "The position value is the Myerson value, in a sense," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(1), pages 47-55, September.
    13. 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.
    14. Jackson, Matthew O., 2005. "Allocation rules for network games," Games and Economic Behavior, Elsevier, vol. 51(1), pages 128-154, April.
    15. Slikker, Marco, 2007. "Bidding for surplus in network allocation problems," Journal of Economic Theory, Elsevier, vol. 137(1), pages 493-511, November.
    16. Manuel, C. & Ortega, E. & del Pozo, M., 2020. "Marginality and Myerson values," European Journal of Operational Research, Elsevier, vol. 284(1), pages 301-312.
    17. A. Ghintran & E. González-Arangüena & C. Manuel, 2012. "A probabilistic position value," Annals of Operations Research, Springer, vol. 201(1), pages 183-196, December.
    18. E. Algaba & J. M. Bilbao & R. Brink & J. J. López, 2012. "The Myerson Value and Superfluous Supports in Union Stable Systems," Journal of Optimization Theory and Applications, Springer, vol. 155(2), pages 650-668, November.
    19. Borkotokey, Surajit & Kumar, Rajnish & Sarangi, Sudipta, 2015. "A solution concept for network games: The role of multilateral interactions," European Journal of Operational Research, Elsevier, vol. 243(3), pages 912-920.
    20. Niharika Kakoty & Surajit Borkotokey & Rajnish Kumar & Abhijit Bora, 2023. "Weighted position value for Network games," Papers 2308.03494, arXiv.org.

    More about this item

    Keywords

    TU game; Graph; Position value; Link game; Graph structure;
    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:apmaco:v:356:y:2019:i:c:p:190-197. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.