IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v103y2020icp69-75.html
   My bibliography  Save this article

Axiomatizations of coalition aggregation functions

Author

Listed:
  • Abe, Takaaki

Abstract

We axiomatize Hart and Kurz’s (1983) two coalition aggregation functions known as the γ-function and the δ-function. A coalition aggregation function is a mapping that assigns a partition to each profile of coalitions selected by players. Through our axiomatization results, we observe that neither the γ-function nor the δ-function satisfies monotonicity. We propose a monotonic function and axiomatically characterize it.

Suggested Citation

  • Abe, Takaaki, 2020. "Axiomatizations of coalition aggregation functions," Mathematical Social Sciences, Elsevier, vol. 103(C), pages 69-75.
    • Handle: RePEc:eee:matsoc:v:103:y:2020:i:c:p:69-75
    DOI: 10.1016/j.mathsocsci.2019.12.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165489619300939
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.mathsocsci.2019.12.001?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. Casajus, André, 2009. "Outside options, component efficiency, and stability," Games and Economic Behavior, Elsevier, vol. 65(1), pages 49-61, January.
    2. Gallo, Oihane & Inarra, Elena, 2018. "Rationing rules and stable coalition structures," Theoretical Economics, Econometric Society, vol. 13(3), September.
    3. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
    4. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-1064, July.
    5. Takaaki Abe, 2018. "Stable coalition structures in symmetric majority games: a coincidence between myopia and farsightedness," Theory and Decision, Springer, vol. 85(3), pages 353-374, October.
    Full references (including those not matched with items on IDEAS)

    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. Elena Parilina & Artem Sedakov, 2016. "Stable Cooperation in a Game with a Major Player," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(02), pages 1-20, June.
    2. Takaaki Abe, 2022. "Stable coalition structures and power indices for majority voting," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(6), pages 1413-1432, December.
    3. Takaaki Abe, 2018. "Stable coalition structures in symmetric majority games: a coincidence between myopia and farsightedness," Theory and Decision, Springer, vol. 85(3), pages 353-374, October.
    4. Agust'in G. Bonifacio & Elena Inarra & Pablo Neme, 2020. "Stable decompositions of coalition formation games," Papers 2009.11689, arXiv.org, revised Dec 2021.
    5. Abe, Takaaki, 2021. "Stability and values for games with coalition structures," Economics Letters, Elsevier, vol. 200(C).
    6. Takaaki Abe, 2019. "Stable Coalition Structures: Characterizations and Applications of Hart and Kurz's Four Stability Concepts," Working Papers 1812, Waseda University, Faculty of Political Science and Economics.
    7. Tobias Hiller, 2023. "Training, Abilities and the Structure of Teams," Games, MDPI, vol. 14(3), pages 1-8, May.
    8. Takaaki Abe, 2019. "Axiomatizations of Coalition Aggregation Functions," Working Papers 1904, Waseda University, Faculty of Political Science and Economics.
    9. Tobias Hiller, 2022. "Abilities and the structure of the firm," International Review of Economics, Springer;Happiness Economics and Interpersonal Relations (HEIRS), vol. 69(3), pages 339-349, September.
    10. Antonio Magaña & Francesc Carreras, 2018. "Coalition Formation and Stability," Group Decision and Negotiation, Springer, vol. 27(3), pages 467-502, June.
    11. Konishi, Hideo & Pan, Chen-Yu, 2021. "Endogenous alliances in survival contests," Journal of Economic Behavior & Organization, Elsevier, vol. 189(C), pages 337-358.
    12. Imamura, Kenzo & Konishi, Hideo & Pan, Chen-Yu, 2023. "Stability in matching with externalities: Pairs competition and oligopolistic joint ventures," Journal of Economic Behavior & Organization, Elsevier, vol. 205(C), pages 270-286.
    13. Ray, Debraj & Vohra, Rajiv, 2015. "Coalition Formation," Handbook of Game Theory with Economic Applications,, Elsevier.
    14. André Casajus, 2010. "Another characterization of the Owen value without the additivity axiom," Theory and Decision, Springer, vol. 69(4), pages 523-536, October.
    15. 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.
    16. Geoffroy de Clippel & Roberto Serrano, 2008. "Marginal Contributions and Externalities in the Value," Econometrica, Econometric Society, vol. 76(6), pages 1413-1436, November.
    17. Barbera, Salvador & Gerber, Anke, 2003. "Corrigendum to "On coalition formation: durable coalition structures": [Mathematical Social Sciences 45 (2003) 185-203]," Mathematical Social Sciences, Elsevier, vol. 46(3), pages 355-356, December.
    18. Kenzo Imamura & Hideo Konishi, 2023. "Assortative Matching with Externalities and Farsighted Agents," Dynamic Games and Applications, Springer, vol. 13(2), pages 497-509, June.
    19. Herings, P. Jean-Jacques & Saulle, Riccardo & Seel, Christian, 2018. "The Last will be First, and the First Last: Segregation in Societies with Positional Externalities," Research Memorandum 027, Maastricht University, Graduate School of Business and Economics (GSBE).
    20. Tobias Hiller, 2018. "The Effects of Excluding Coalitions," Games, MDPI, vol. 9(1), pages 1-7, January.

    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:eee:matsoc:v:103:y:2020:i:c:p:69-75. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505565 .

    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.