IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v109y2002i1p143-15810.1023-a1016348001805.html
   My bibliography  Save this article

Generating Functions for Computing the Myerson Value

Author

Listed:
  • J.R. Fernández
  • E. Algaba
  • J.M. Bilbao
  • A. Jiménez
  • N. Jiménez
  • J.J. López

Abstract

The complexity of a computational problem is the order of computational resources which are necessary and sufficient to solve the problem. The algorithm complexity is the cost of a particular algorithm. We say that a problem has polynomial complexity if its computational complexity is a polynomial in the measure of input size. We introduce polynomial time algorithms based in generating functions for computing the Myerson value in weighted voting games restricted by a tree. Moreover, we apply the new generating algorithm for computing the Myerson value in the Council of Ministers of the European Union restricted by a communication structure. Copyright Kluwer Academic Publishers 2002

Suggested Citation

  • J.R. Fernández & E. Algaba & J.M. Bilbao & A. Jiménez & N. Jiménez & J.J. López, 2002. "Generating Functions for Computing the Myerson Value," Annals of Operations Research, Springer, vol. 109(1), pages 143-158, January.
    • Handle: RePEc:spr:annopr:v:109:y:2002:i:1:p:143-158:10.1023/a:1016348001805
    DOI: 10.1023/A:1016348001805
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1023/A:1016348001805
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1023/A:1016348001805?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.

    Citations

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


    Cited by:

    1. Michela Chessa, 2014. "A generating functions approach for computing the Public Good index efficiently," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 658-673, July.
    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.
    3. Luisa Monroy & Francisco Fernández, 2014. "Banzhaf index for multiple voting systems. An application to the European Union," Annals of Operations Research, Springer, vol. 215(1), pages 215-230, April.
    4. Antônio Francisco Neto & Carolina Rodrigues Fonseca, 2019. "An approach via generating functions to compute power indices of multiple weighted voting games with incompatible players," Annals of Operations Research, Springer, vol. 279(1), pages 221-249, August.
    5. J. R. Fernández & I. Gallego & A. Jiménez-Losada & M. Ordóñez, 2019. "The cg-average tree value for games on cycle-free fuzzy communication structures," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 456-478, October.
    6. Alonso-Meijide, J.M. & Casas-Méndez, B. & Fiestras-Janeiro, M.G., 2015. "Computing Banzhaf–Coleman and Shapley–Shubik power indices with incompatible players," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 377-387.
    7. Martí Jané Ballarín, 2023. "The complexity of power indices in voting games with incompatible players," UB School of Economics Working Papers 2023/441, University of Barcelona School of Economics.
    8. Constandina Koki & Stefanos Leonardos, 2019. "Coalitions and Voting Power in the Greek Parliament of 2012: A Case-Study," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 35(4), pages 295-313, April.
    9. Benati, Stefano & Rizzi, Romeo & Tovey, Craig, 2015. "The complexity of power indexes with graph restricted coalitions," Mathematical Social Sciences, Elsevier, vol. 76(C), pages 53-63.
    10. Stefano Benati & Giuseppe Vittucci Marzetti, 2021. "Voting power on a graph connected political space with an application to decision-making in the Council of the European Union," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(4), pages 733-761, November.
    11. Alonso-Meijide, J.M. & Bilbao, J.M. & Casas-Méndez, B. & Fernández, J.R., 2009. "Weighted multiple majority games with unions: Generating functions and applications to the European Union," European Journal of Operational Research, Elsevier, vol. 198(2), pages 530-544, October.
    12. Antônio Francisco Neto, 2019. "Generating Functions of Weighted Voting Games, MacMahon’s Partition Analysis, and Clifford Algebras," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 74-101, February.
    13. Karl Ortmann, 2013. "A cooperative value in a multiplicative model," 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. 21(3), pages 561-583, September.

    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:109:y:2002:i:1:p:143-158:10.1023/a:1016348001805. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.