IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v93y2021i3d10.1007_s00186-021-00743-z.html
   My bibliography  Save this article

New axiomatizations of the Owen value

Author

Listed:
  • Xun-Feng Hu

    (Guangzhou University)

Abstract

In this paper, we propose three new axiomatizations of the Owen value, similar as the axiomatizations of the Shapley value of Chun (Int J Game Theory 20(2):183–190, 1991), van den Brink (Int J Game Theory 30(3):309–319, 2002), and Manuel et al. (Math Methods Oper Res 77:1–14, 2013), respectively. Firstly, we show that the additivity and null player property in Owen’s (in: Henn and Moeschlin (eds) Mathematical economics and game theory, Springer-Verlog, Berlin, 1977) axiomatization can be weakened into coalitional strategic equivalence. And then, we prove that the coalitional symmetry (respectively symmetry within union) and additivity in Owen’s (in: Henn and Moeschlin (eds) Mathematical economics and game theory, Springer-Verlog, Berlin, 1977) axiomatization can be weakened into a variation of fairness, named as coalitional fairness (respectively fairness within union). Finally, we show that the two fairness axioms in our second axiomatization can be weakened into two axioms, involving a special relation between players, named as indifference. Besides characterizing the Owen value, we also illustrate that our results can be extended to the Winter value, being a common single-valued solution for cooperative games with a level structure.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:93:y:2021:i:3:d:10.1007_s00186-021-00743-z
    DOI: 10.1007/s00186-021-00743-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00186-021-00743-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00186-021-00743-z?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. Levy, Anat & Mclean, Richard P., 1989. "Weighted coalition structure values," Games and Economic Behavior, Elsevier, vol. 1(3), pages 234-249, September.
    2. René van den Brink, 2002. "An axiomatization of the Shapley value using a fairness property," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(3), pages 309-319.
    3. 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.
    4. Chun, Youngsub, 1991. "On the Symmetric and Weighted Shapley Values," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(2), pages 183-190.
    5. Xun-Feng Hu, 2020. "The weighted Shapley-egalitarian value for cooperative games with a coalition structure," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 193-212, April.
    6. André Casajus, 2010. "Another characterization of the Owen value without the additivity axiom," Theory and Decision, Springer, vol. 69(4), pages 523-536, October.
    7. André Casajus, 2011. "Differential marginality, van den Brink fairness, and the Shapley value," Theory and Decision, Springer, vol. 71(2), pages 163-174, August.
    8. AUMANN, Robert J. & DREZE, Jacques H., 1974. "Cooperative games with coalition structures," LIDAM Reprints CORE 217, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. José Alonso-Meijide & M. Fiestras-Janeiro, 2002. "Modification of the Banzhaf Value for Games with a Coalition Structure," Annals of Operations Research, Springer, vol. 109(1), pages 213-227, January.
    10. 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.
    11. 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.
    12. Martin Shubik, 1962. "Incentives, Decentralized Control, the Assignment of Joint Costs and Internal Pricing," Management Science, INFORMS, vol. 8(3), pages 325-343, April.
    13. Winter, Eyal, 1992. "The consistency and potential for values of games with coalition structure," Games and Economic Behavior, Elsevier, vol. 4(1), pages 132-144, January.
    14. 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.
    15. Emilio Calvo & Esther Gutiérrez, 2013. "The Shapley-Solidarity Value For Games With A Coalition Structure," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 1-24.
    16. Jean J. M. Derks & Hans H. Haller, 1999. "Null Players Out? Linear Values For Games With Variable Supports," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 1(03n04), pages 301-314.
    17. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    18. Casajus, André, 2014. "The Shapley value without efficiency and additivity," Mathematical Social Sciences, Elsevier, vol. 68(C), pages 1-4.
    19. 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.
    20. Chun, Youngsub, 1989. "A new axiomatization of the shapley value," Games and Economic Behavior, Elsevier, vol. 1(2), pages 119-130, 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. Sylvain Béal & Marc Deschamps & Mostapha Diss & Rodrigue Tido Takeng, 2024. "Cooperative games with diversity constraints," Working Papers hal-04447373, HAL.
    2. 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.
    3. André Casajus & Rodrigue Tido Takeng, 2022. "Second-order productivity, second-order payoffs, and the Owen value," Post-Print hal-03798448, HAL.
    4. Zijun Li & Fanyong Meng, 2023. "The potential and consistency of the Owen value for fuzzy cooperative games with a coalition structure," Fuzzy Optimization and Decision Making, Springer, vol. 22(3), pages 387-414, 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. Manfred Besner, 2022. "Harsanyi support levels solutions," Theory and Decision, Springer, vol. 93(1), pages 105-130, July.
    2. 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.
    3. Besner, Manfred, 2017. "Weighted Shapley levels values," MPRA Paper 82978, University Library of Munich, Germany.
    4. André Casajus & Rodrigue Tido Takeng, 2022. "Second-order productivity, second-order payoffs, and the Owen value," Post-Print hal-03798448, HAL.
    5. 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.
    6. Sylvain Béal & Marc Deschamps & Mostapha Diss & Rodrigue Tido Takeng, 2024. "Cooperative games with diversity constraints," Working Papers hal-04447373, HAL.
    7. Besner, Manfred, 2018. "The weighted Shapley support levels values," MPRA Paper 87617, University Library of Munich, Germany.
    8. Xun-Feng Hu, 2020. "The weighted Shapley-egalitarian value for cooperative games with a coalition structure," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 193-212, April.
    9. 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.
    10. Besner, Manfred, 2018. "Weighted Shapley hierarchy levels values," MPRA Paper 88160, University Library of Munich, Germany.
    11. 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.
    12. Besner, Manfred, 2018. "Two classes of weighted values for coalition structures with extensions to level structures," MPRA Paper 87742, University Library of Munich, Germany.
    13. Takaaki Abe & Satoshi Nakada, 2019. "The weighted-egalitarian Shapley values," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(2), pages 197-213, February.
    14. 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.
    15. 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.
    16. Vidal-Puga, Juan, 2012. "The Harsanyi paradox and the “right to talk” in bargaining among coalitions," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 214-224.
    17. Jun Su & Yuan Liang & Guangmin Wang & Genjiu Xu, 2020. "Characterizations, Potential, and an Implementation of the Shapley-Solidarity Value," Mathematics, MDPI, vol. 8(11), pages 1-20, November.
    18. Sylvain Béal & Mostapha Diss & Rodrigue Tido Takeng, 2024. "New axiomatizations of the Diversity Owen and Shapley values," Working Papers 2024-09, CRESE.
    19. Rong Zou & Genjiu Xu & Wenzhong Li & Xunfeng Hu, 2020. "A coalitional compromised solution for cooperative games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(4), pages 735-758, December.
    20. Besner, Manfred, 2023. "The per capita Shapley support levels value," MPRA Paper 116457, University Library of Munich, Germany.

    More about this item

    Keywords

    Cooperative game; Coalition structure; Owen value; Shapley value; Winter value; Level structure;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

    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:93:y:2021:i:3:d:10.1007_s00186-021-00743-z. 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.