IDEAS home Printed from https://ideas.repec.org/a/spr/jogath/v30y2002i3p377-404.html
   My bibliography  Save this article

Linear and symmetric allocation methods for partially defined cooperative games

Author

Listed:
  • David Housman

    (Department of Mathematics, Goshen College, 1700 South Main Street, Goshen, IN 46526, USA)

Abstract

A partially defined cooperative game is a coalition function form game in which some of the coalitional worths are not known. An application would be cost allocation of a joint project among so many players that the determination of all coalitional worths is prohibitive. This paper generalizes the concept of the Shapley value for cooperative games to the class of partially defined cooperative games. Several allocation method characterization theorems are given utilizing linearity, symmetry, formulation independence, subsidy freedom, and monotonicity properties. Whether a value exists or is unique depends crucially on the class of games under consideration.

Suggested Citation

  • David Housman, 2002. "Linear and symmetric allocation methods for partially defined cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(3), pages 377-404.
    • Handle: RePEc:spr:jogath:v:30:y:2002:i:3:p:377-404
    Note: Received June 1996/Revised August 2001
    as

    Download full text from publisher

    File URL: http://link.springer.de/link/service/journals/00182/papers/2030003/20300377.pdf
    Download Restriction: Access to the full text of the articles in this series is restricted
    ---><---

    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. Curiel, I. & Potters, J.A.M. & Rajendra Prasad, V. & Tijs, S.H. & Veltman, B., 1993. "Cooperation in one machine scheduling," Other publications TiSEM 9c5ceec5-2080-4b5c-98d5-0, Tilburg University, School of Economics and Management.
    2. Gilboa, Itzhak & Monderer, Dov, 1991. "Quasi-values on Subspaces," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(4), pages 353-363.
    3. Nowak, A.S. & Radzik, T., 1995. "On axiomatizations of the weighted Shapley values," Games and Economic Behavior, Elsevier, vol. 8(2), pages 389-405.
    4. Pradeep Dubey & Abraham Neyman & Robert J. Weber, 1979. "Value Theory without Efficiency," Cowles Foundation Discussion Papers 513, Cowles Foundation for Research in Economics, Yale University.
    5. Monderer, Dov, 1988. "Values and Semivalues on Subspaces of Finite Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(4), pages 301-310.
    6. Willson, Stephen J, 1993. "A Value for Partially Defined Cooperative Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(4), pages 371-384.
    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. Tobias Hiller, 2013. "The distribution of power in governing coalitions of the German Laender," Applied Economics Letters, Taylor & Francis Journals, vol. 20(12), pages 1155-1159, August.
    2. Satoshi Masuya, 2023. "Two Approaches to Estimate the Shapley Value for Convex Partially Defined Games," Mathematics, MDPI, vol. 12(1), pages 1-15, December.
    3. Satoshi Masuya & Masahiro Inuiguchi, 2016. "A fundamental study for partially defined cooperative games," Fuzzy Optimization and Decision Making, Springer, vol. 15(3), pages 281-306, September.

    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. Giulia Cesari & Roberto Lucchetti & Stefano Moretti, 2017. "Generalized additive games," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 919-939, November.
    2. Donald Nganmegni Njoya & Issofa Moyouwou & Nicolas Gabriel Andjiga, 2021. "The equal-surplus Shapley value for chance-constrained games on finite sample spaces," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(3), pages 463-499, June.
    3. Saari, Donald G. & Sieberg, Katri K., 2001. "Some Surprising Properties of Power Indices," Games and Economic Behavior, Elsevier, vol. 36(2), pages 241-263, August.
    4. Fujimoto, Katsushige & Kojadinovic, Ivan & Marichal, Jean-Luc, 2006. "Axiomatic characterizations of probabilistic and cardinal-probabilistic interaction indices," Games and Economic Behavior, Elsevier, vol. 55(1), pages 72-99, April.
    5. Lange, Fabien & Grabisch, Michel, 2009. "Values on regular games under Kirchhoff's laws," Mathematical Social Sciences, Elsevier, vol. 58(3), pages 322-340, November.
    6. Susana López & Martha Saboya, 2009. "On the relationship between Shapley and Owen values," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 17(4), pages 415-423, December.
    7. Manfred Besner, 2022. "Harsanyi support levels solutions," Theory and Decision, Springer, vol. 93(1), pages 105-130, July.
    8. Borm, Peter & Fiestras-Janeiro, Gloria & Hamers, Herbert & Sanchez, Estela & Voorneveld, Mark, 2002. "On the convexity of games corresponding to sequencing situations with due dates," European Journal of Operational Research, Elsevier, vol. 136(3), pages 616-634, February.
    9. Radzik, Tadeusz, 2012. "A new look at the role of players’ weights in the weighted Shapley value," European Journal of Operational Research, Elsevier, vol. 223(2), pages 407-416.
    10. O'Neill, Barry & Peleg, Bezalel, 2008. "Lexicographic composition of simple games," Games and Economic Behavior, Elsevier, vol. 62(2), pages 628-642, March.
    11. M. Musegaas & P. E. M. Borm & M. Quant, 2018. "On the convexity of step out–step in sequencing games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 68-109, April.
    12. Dubey, Pradeep & Einy, Ezra & Haimanko, Ori, 2005. "Compound voting and the Banzhaf index," Games and Economic Behavior, Elsevier, vol. 51(1), pages 20-30, April.
    13. Casajus, André & Huettner, Frank, 2014. "Weakly monotonic solutions for cooperative games," Journal of Economic Theory, Elsevier, vol. 154(C), pages 162-172.
    14. Ruiz, Luis M. & Valenciano, Federico & Zarzuelo, Jose M., 1998. "The Family of Least Square Values for Transferable Utility Games," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 109-130, July.
    15. Geoffroy de Clippel & Roberto Serrano, 2008. "Marginal Contributions and Externalities in the Value," Econometrica, Econometric Society, vol. 76(6), pages 1413-1436, November.
    16. Casajus, André, 2018. "Symmetry, mutual dependence, and the weighted Shapley values," Journal of Economic Theory, Elsevier, vol. 178(C), pages 105-123.
    17. Musegaas, M. & Borm, P.E.M. & Quant, M., 2015. "Step out–Step in sequencing games," European Journal of Operational Research, Elsevier, vol. 246(3), pages 894-906.
    18. Rafael Amer & José Miguel giménez, 2003. "Modification of Semivalues for Games with Coalition Structures," Theory and Decision, Springer, vol. 54(3), pages 185-205, May.
    19. Annick Laruelle & Federico Valenciano, 2005. "A critical reappraisal of some voting power paradoxes," Public Choice, Springer, vol. 125(1), pages 17-41, July.
    20. Manfred Besner, 2019. "Axiomatizations of the proportional Shapley value," Theory and Decision, Springer, vol. 86(2), pages 161-183, March.

    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:jogath:v:30:y:2002:i:3:p:377-404. 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.