IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v137y2005i1p141-16010.1007-s10479-005-2251-x.html
   My bibliography  Save this article

Values for Interior Operator Games

Author

Listed:
  • J. Bilbao
  • A. Jiménez-Losada
  • E. Lebrón
  • C. Chacón

Abstract

The aim of this paper is to study a new class of cooperative games called interior operator games. These games are additive games restricted by antimatroids. We consider several types of cooperative games as peer group games, big boss games, clan games and information market games and show that all of them are interior operator games. Next, we analyze the properties of these games and compute the Shapley, Banzhaf and Tijs values. Copyright Springer Science + Business Media, Inc. 2005

Suggested Citation

  • J. Bilbao & A. Jiménez-Losada & E. Lebrón & C. Chacón, 2005. "Values for Interior Operator Games," Annals of Operations Research, Springer, vol. 137(1), pages 141-160, July.
    • Handle: RePEc:spr:annopr:v:137:y:2005:i:1:p:141-160:10.1007/s10479-005-2251-x
    DOI: 10.1007/s10479-005-2251-x
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-005-2251-x
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-005-2251-x?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. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    2. 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.
    3. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, April.
    4. 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)

    Citations

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


    Cited by:

    1. J. Bilbao & C. Chacón & A. Jiménez-Losada & E. Lebrón, 2008. "Convexity properties for interior operator games," Annals of Operations Research, Springer, vol. 158(1), pages 117-131, February.
    2. Jiménez-Losada, A. & Chacón, C. & Lebrón, E., 2012. "Linear values for interior operator games," European Journal of Operational Research, Elsevier, vol. 220(1), pages 182-186.
    3. René van den Brink & Ilya Katsev & Gerard van der Laan, 2008. "An Algorithm for Computing the Nucleolus of Disjunctive Additive Games with An Acyclic Permission Structure," Tinbergen Institute Discussion Papers 08-104/1, Tinbergen Institute.
    4. 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.

    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. Suzuki, T. & Talman, A.J.J., 2011. "Solution Concepts for Cooperative Games with Circular Communication Structure," Discussion Paper 2011-100, Tilburg University, Center for Economic Research.
    2. Bilbao, J. M., 1998. "Axioms for the Shapley value on convex geometries," European Journal of Operational Research, Elsevier, vol. 110(2), pages 368-376, October.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Michel Grabisch, 2013. "The core of games on ordered structures and graphs," Annals of Operations Research, Springer, vol. 204(1), pages 33-64, April.
    8. 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.
    9. 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.
    10. Encarnaciön Algaba & Sylvain Béal & Eric Rémila & Phillippe Solal, 2018. "Harsanyi power solutions for cooperative games on voting structures," Working Papers 2018-05, CRESE.
    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. Encarnacion Algaba & Rene van den Brink, 2019. "The Shapley Value and Games with Hierarchies," Tinbergen Institute Discussion Papers 19-064/II, Tinbergen Institute.
    13. Encarnacion Algaba & Rene van den Brink, 2021. "Networks, Communication and Hierarchy: Applications to Cooperative Games," Tinbergen Institute Discussion Papers 21-019/IV, Tinbergen Institute.
    14. Bilbao, J. M. & Lebron, E. & Jimenez, N., 1999. "The core of games on convex geometries," European Journal of Operational Research, Elsevier, vol. 119(2), pages 365-372, December.
    15. 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.
    16. Daniel Li Li & Erfang Shan, 2021. "Cooperative games with partial information," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 297-309, March.
    17. René van den Brink & Gerard van der Laan & Valeri Vasil'ev, 2007. "Distributing Dividends in Games with Ordered Players," Tinbergen Institute Discussion Papers 06-114/1, Tinbergen Institute.
    18. René van den Brink & Gerard van der Laan & Valeri Vasil'ev, 0000. "The Restricted Core for Totally Positive Games with Ordered Players," Tinbergen Institute Discussion Papers 09-038/1, Tinbergen Institute.
    19. Labreuche, Christophe, 2011. "Interaction indices for games on combinatorial structures with forbidden coalitions," European Journal of Operational Research, Elsevier, vol. 214(1), pages 99-108, October.
    20. 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.

    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:annopr:v:137:y:2005:i:1:p:141-160:10.1007/s10479-005-2251-x. 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.