IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v63y2006i3p435-442.html
   My bibliography  Save this article

The Shapley Valuation Function for Strategic Games in which Players Cooperate

Author

Listed:
  • Luisa Carpente
  • Balbina Casas-Méndez
  • Ignacio García-Jurado
  • Anne Nouweland

Abstract

In this note we use the Shapley value to define a valuation function. A valuation function associates with every non-empty coalition of players in a strategic game a vector of payoffs for the members of the coalition that provides these players’ valuations of cooperating in the coalition. The Shapley valuation function is defined using the lower-value based method to associate coalitional games with strategic games that was introduced in Carpente et al. (2005). We discuss axiomatic characterizations of the Shapley valuation function. Copyright Springer-Verlag 2006

Suggested Citation

  • Luisa Carpente & Balbina Casas-Méndez & Ignacio García-Jurado & Anne Nouweland, 2006. "The Shapley Valuation Function for Strategic Games in which Players Cooperate," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(3), pages 435-442, July.
    • Handle: RePEc:spr:mathme:v:63:y:2006:i:3:p:435-442
    DOI: 10.1007/s00186-005-0028-2
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00186-005-0028-2
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00186-005-0028-2?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. Luisa Carpente & Balbina Casas-Méndez & Ignacio García-Jurado & Anne van den Nouweland, 2005. "Values for strategic games in which players cooperate," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(3), pages 397-419, September.
    2. van Damme, E.E.C., 2002. "Game theory and the market," Other publications TiSEM b167b13f-ef75-4003-b410-4, Tilburg University, School of Economics and Management.
    3. Montero, M.P., 2000. "Endogenous coalition formation and bargaining," Other publications TiSEM 5e5fcfcf-8c30-4856-a2e8-4, Tilburg University, School of Economics and Management.
    4. Norde, Henk & Voorneveld, Mark, 2004. "Characterizations of the value of matrix games," Mathematical Social Sciences, Elsevier, vol. 48(2), pages 193-206, September.
    5. Shapley, Lloyd S. & Shubik, Martin, 1969. "On market games," Journal of Economic Theory, Elsevier, vol. 1(1), pages 9-25, 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. Ignacio García-Jurado, 2008. "Comments on: Transversality of the Shapley value," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(1), pages 51-53, July.

    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. Anne van den Nouweland, 2011. "Comments on: 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 29-32, July.
    2. Avishay Aiche, 2019. "On the equal treatment imputations subset in the bargaining set for smooth vector-measure games with a mixed measure space of players," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(2), pages 411-421, June.
    3. Judith Timmer & Werner Scheinhardt, 2018. "Customer and Cost Sharing in a Jackson Network," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 20(03), pages 1-10, September.
    4. Kovalenkov, A. & Holtz Wooders, M., 1997. "Epsilon Cores of Games and Economies With Limited Side Payments," UFAE and IAE Working Papers 392.97, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    5. Sun, Ning & Trockel, Walter & Yang, Zaifu, 2008. "Competitive outcomes and endogenous coalition formation in an n-person game," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 853-860, July.
    6. Imre Fertő & László Á Kóczy & Attila Kovács & Balázs R Sziklai, 0. "The power ranking of the members of the Agricultural Committee of the European Parliament," European Review of Agricultural Economics, Oxford University Press and the European Agricultural and Applied Economics Publications Foundation, vol. 47(5), pages 1897-1919.
    7. Csóka Péter & Pintér Miklós, 2016. "On the Impossibility of Fair Risk Allocation," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 16(1), pages 143-158, January.
    8. Pálvölgyi, Dénes & Peters, Hans & Vermeulen, Dries, 2014. "A strategic approach to multiple estate division problems," Games and Economic Behavior, Elsevier, vol. 88(C), pages 135-152.
    9. Lahiri, Somdeb, 2008. "Manipulation of market equilibrium via endowments," MPRA Paper 10002, University Library of Munich, Germany.
    10. Qin, Cheng-Zhong & Shapley, Lloyd S. & Shimomura, Ken-Ichi, 2006. "The Walras core of an economy and its limit theorem," Journal of Mathematical Economics, Elsevier, vol. 42(2), pages 180-197, April.
    11. Kóczy, LászlóÁ., 2015. "Stationary consistent equilibrium coalition structures constitute the recursive core," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 104-110.
    12. Alparslan-Gok, S.Z. & Miquel, S. & Tijs, S.H., 2008. "Cooperation under Interval Uncertainty," Other publications TiSEM 9a01bd57-964d-4e71-8508-7, Tilburg University, School of Economics and Management.
    13. Gong, X., 2001. "Empirical studies on the labor market and on consumer demand," Other publications TiSEM eed29455-f1bf-4cc3-aff5-c, Tilburg University, School of Economics and Management.
    14. Hayashi, Fumio & Matsui, Akihiko, 1996. "A Model of Fiat Money and Barter," Journal of Economic Theory, Elsevier, vol. 68(1), pages 111-132, January.
    15. Martin Shubik & Myrna Holtz Wooders, 1982. "Approximate Cores of a General Class of Economies: Part II. Set-Up Costs and Firm Formation in Coalition Production Economies," Cowles Foundation Discussion Papers 619, Cowles Foundation for Research in Economics, Yale University.
    16. Abraham Neyman & Rann Smorodinsky, 2004. "Asymptotic Values of Vector Measure Games," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 739-775, November.
    17. Borrero, D.V. & Hinojosa, M.A. & Mármol, A.M., 2016. "DEA production games and Owen allocations," European Journal of Operational Research, Elsevier, vol. 252(3), pages 921-930.
    18. van Damme, E.E.C., 2002. "Game theory and the market," Other publications TiSEM b167b13f-ef75-4003-b410-4, Tilburg University, School of Economics and Management.
    19. Debraj Ray & Rajiv Vohra, 2015. "The Farsighted Stable Set," Econometrica, Econometric Society, vol. 83(3), pages 977-1011, May.
    20. Krzysztof J. Szajowski, 2020. "Rationalization of detection of the multiple disorders," Statistical Papers, Springer, vol. 61(4), pages 1545-1563, August.

    More about this item

    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:63:y:2006:i:3:p:435-442. 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.