IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v66y2007i2p255-261.html
   My bibliography  Save this article

Owen coalitional value without additivity axiom

Author

Listed:
  • Anna Khmelnitskaya
  • Elena Yanovskaya

Abstract

We show that the Owen value for TU games with coalition structure can be characterized without the additivity axiom similarly as it was done by Young for the Shapley value for general TU games. Our axiomatization via four axioms of efficiency, marginality, symmetry across coalitions, and symmetry within coalitions is obtained from the original Owen’s one by the replacement of additivity and null-player via marginality. We show that the alike axiomatization for the generalization of the Owen value suggested by Winter for games with level structure is valid as well. Copyright Springer-Verlag 2007

Suggested Citation

  • Anna Khmelnitskaya & Elena Yanovskaya, 2007. "Owen coalitional value without additivity axiom," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(2), pages 255-261, October.
    • Handle: RePEc:spr:mathme:v:66:y:2007:i:2:p:255-261
    DOI: 10.1007/s00186-006-0119-8
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00186-006-0119-8
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00186-006-0119-8?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. Winter, Eyal, 1989. "A Value for Cooperative Games with Levels Structure of Cooperation," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(2), pages 227-240.
    2. Anna B. Khmelnitskaya, 2003. "Shapley value for constant-sum games," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(2), pages 223-227, December.
    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. Sylvain Béal & Marc Deschamps & Mostapha Diss & Rodrigue Tido Takeng, 2024. "Cooperative games with diversity constraints," Working Papers hal-04447373, HAL.
    2. Riccardo Ferretti & Giovanni Gallo & Andrea Landi & Valeria Venturelli, 2018. "Market-Book Ratios of European Banks: What Does Explain the Structural Fall?," Centro Studi di Banca e Finanza (CEFIN) (Center for Studies in Banking and Finance) 18011, Universita di Modena e Reggio Emilia, Dipartimento di Economia "Marco Biagi".
    3. Meng, Fanyong & Chen, Xiaohong & Zhang, Qiang, 2015. "A coalitional value for games on convex geometries with a coalition structure," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 605-614.
    4. Abe, Takaaki & Nakada, Satoshi, 2023. "The in-group egalitarian Owen values," Games and Economic Behavior, Elsevier, vol. 142(C), pages 1-16.
    5. Pulido, Manuel A. & Sánchez-Soriano, Joaquín, 2009. "On the core, the Weber set and convexity in games with a priori unions," European Journal of Operational Research, Elsevier, vol. 193(2), pages 468-475, March.
    6. Knezevic, David & Krüger, Niclas & Nordström, Martin, 2019. "A Guarantee – Does the Obligee Agree? A Risk Premium Decomposition of Sub-Sovereign Bond Spreads," Working Papers 2019:12, Örebro University, School of Business.
    7. C. Manuel & E. González-Arangüena & R. Brink, 2013. "Players indifferent to cooperate and characterizations of the Shapley value," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(1), pages 1-14, February.
    8. André Casajus & Rodrigue Tido Takeng, 2023. "Second-order productivity, second-order payoffs, and the Owen value," Annals of Operations Research, Springer, vol. 320(1), pages 1-13, January.
    9. Riccardo Ferretti & Giovanni Gallo & Andrea Landi & Valeria Venturelli, 2018. "Market-Book Ratios of European Banks: What Does Explain the Structural Fall?," Centro Studi di Banca e Finanza (CEFIN) (Center for Studies in Banking and Finance) 0065, Universita di Modena e Reggio Emilia, Dipartimento di Economia "Marco Biagi".
    10. Guangming Wang & Zeguang Cui & Erfang Shan, 2022. "An Axiomatization of the Value α for Games Restricted by Augmenting Systems," Mathematics, MDPI, vol. 10(15), pages 1-9, August.
    11. Michael Jones & Jennifer Wilson, 2013. "Two-step coalition values for multichoice games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(1), pages 65-99, February.
    12. Besner, Manfred, 2017. "Weighted Shapley levels values," MPRA Paper 82978, University Library of Munich, Germany.
    13. André Casajus, 2010. "Another characterization of the Owen value without the additivity axiom," Theory and Decision, Springer, vol. 69(4), pages 523-536, October.
    14. Gómez-Rúa, María & Vidal-Puga, Juan, 2010. "The axiomatic approach to three values in games with coalition structure," European Journal of Operational Research, Elsevier, vol. 207(2), pages 795-806, December.
    15. J. C. Gonçalves-Dosantos & I. García-Jurado & J. Costa & J. M. Alonso-Meijide, 2022. "Necessary players and values," Annals of Operations Research, Springer, vol. 318(2), pages 935-961, November.
    16. André Casajus & Rodrigue Tido Takeng, 2022. "Second-order productivity, second-order payoffs, and the Owen value," Post-Print hal-03798448, HAL.
    17. Manfred Besner, 2022. "Harsanyi support levels solutions," Theory and Decision, Springer, vol. 93(1), pages 105-130, July.
    18. Besner, Manfred, 2018. "The weighted Shapley support levels values," MPRA Paper 87617, University Library of Munich, Germany.
    19. Erfang Shan, 2023. "Marginality and a Characterization of the Owen Graph value," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(2), pages 451-461, June.
    20. Xun-Feng Hu & Deng-Feng Li, 2021. "The Equal Surplus Division Value for Cooperative Games with a Level Structure," Group Decision and Negotiation, Springer, vol. 30(6), pages 1315-1341, December.
    21. Xun-Feng Hu, 2021. "New axiomatizations of the Owen value," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(3), pages 585-603, June.
    22. Silvia Lorenzo-Freire, 2017. "New characterizations of the Owen and Banzhaf–Owen values using the intracoalitional balanced contributions property," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 579-600, October.
    23. Hüttner, Frank & Sunder, Marco, 2011. "Decomposing R2 with the Owen value," Working Papers 100, University of Leipzig, Faculty of Economics and Management Science.
    24. Besner, Manfred, 2023. "The per capita Shapley support levels value," MPRA Paper 116457, University Library of Munich, Germany.

    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. Antonio Magaña & Francesc Carreras, 2018. "Coalition Formation and Stability," Group Decision and Negotiation, Springer, vol. 27(3), pages 467-502, June.
    2. J. M. Alonso-Meijide & J. Costa & I. García-Jurado & J. C. Gonçalves-Dosantos, 2023. "On egalitarian values for cooperative games with level structures," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 98(1), pages 57-73, August.
    3. Csóka, Péter & Illés, Ferenc & Solymosi, Tamás, 2022. "On the Shapley value of liability games," European Journal of Operational Research, Elsevier, vol. 300(1), pages 378-386.
    4. Tejada, O. & Álvarez-Mozos, M., 2018. "Graphs and (levels of) cooperation in games: Two ways how to allocate the surplus," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 114-122.
    5. André Casajus, 2010. "Another characterization of the Owen value without the additivity axiom," Theory and Decision, Springer, vol. 69(4), pages 523-536, October.
    6. Manfred Besner, 2022. "Harsanyi support levels solutions," Theory and Decision, Springer, vol. 93(1), pages 105-130, July.
    7. Calvo, Emilio & Javier Lasaga, J. & Winter, Eyal, 1996. "The principle of balanced contributions and hierarchies of cooperation," Mathematical Social Sciences, Elsevier, vol. 31(3), pages 171-182, June.
    8. Kongo, Takumi, 2011. "Value of games with two-layered hypergraphs," Mathematical Social Sciences, Elsevier, vol. 62(2), pages 114-119, September.
    9. Nils Roehl, 2013. "Two-Stage Allocation Rules," Working Papers Dissertations 01, Paderborn University, Faculty of Business Administration and Economics.
    10. Yoshio Kamijo, 2013. "The collective value: a new solution for games with coalition structures," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 572-589, October.
    11. Tobias Hiller, 2021. "Hierarchy and the size of a firm," International Review of Economics, Springer;Happiness Economics and Interpersonal Relations (HEIRS), vol. 68(3), pages 389-404, September.
    12. Tobias Hiller, 2018. "The Effects of Excluding Coalitions," Games, MDPI, vol. 9(1), pages 1-7, January.
    13. Besner, Manfred, 2018. "Weighted Shapley hierarchy levels values," MPRA Paper 88160, University Library of Munich, Germany.
    14. María Gómez-Rúa & Juan Vidal-Puga, 2011. "Balanced per capita contributions and level structure of cooperation," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 167-176, July.
    15. Besner, Manfred, 2017. "Weighted Shapley levels values," MPRA Paper 82978, University Library of Munich, Germany.
    16. Álvarez-Mozos, M. & van den Brink, R. & van der Laan, G. & Tejada, O., 2013. "Share functions for cooperative games with levels structure of cooperation," European Journal of Operational Research, Elsevier, vol. 224(1), pages 167-179.
    17. André Casajus & Rodrigue Tido Takeng, 2022. "Second-order productivity, second-order payoffs, and the Owen value," Post-Print hal-03798448, HAL.
    18. Valencia-Toledo, Alfredo & Vidal-Puga, Juan, 2023. "A linear model for freight transportation," MPRA Paper 119301, University Library of Munich, Germany.
    19. Gómez-Rúa, María & Vidal-Puga, Juan, 2010. "The axiomatic approach to three values in games with coalition structure," European Journal of Operational Research, Elsevier, vol. 207(2), pages 795-806, December.
    20. René Brink & Anna Khmelnitskaya & Gerard Laan, 2016. "An Owen-type value for games with two-level communication structure," Annals of Operations Research, Springer, vol. 243(1), pages 179-198, August.

    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:66:y:2007:i:2:p:255-261. 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.