IDEAS home Printed from https://ideas.repec.org/p/wap/wpaper/1904.html
   My bibliography  Save this paper

Axiomatizations of Coalition Aggregation Functions

Author

Listed:
  • Takaaki Abe

    (School of Political Science and Economics, Waseda University)

Abstract

We axiomatize Hart and Kurz's (1983) two coalition aggregation functions known as the γfunction and the δ-function. A coalition aggregation function is a mapping that assigns a partition to each coalition profile, where a coalition profile is a vector of coalitions selected by all 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. An impossibility result on monotonicity is also provided.

Suggested Citation

  • Takaaki Abe, 2019. "Axiomatizations of Coalition Aggregation Functions," Working Papers 1904, Waseda University, Faculty of Political Science and Economics.
    • Handle: RePEc:wap:wpaper:1904
    as

    Download full text from publisher

    File URL: https://www.waseda.jp/fpse/winpec/assets/uploads/2019/04/WP_E1904.pdf
    File Function: First version,
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Koczy, Laszlo A. & Lauwers, Luc, 2004. "The coalition structure core is accessible," Games and Economic Behavior, Elsevier, vol. 48(1), pages 86-93, July.
    2. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
    3. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-1064, July.
    4. 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. Abe, Takaaki, 2020. "Axiomatizations of coalition aggregation functions," Mathematical Social Sciences, Elsevier, vol. 103(C), pages 69-75.
    2. 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.
    3. 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.
    4. Takaaki Abe & Yukihiko Funaki, 2021. "The projective core of symmetric games with externalities," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 167-183, March.
    5. Ray, Debraj & Vohra, Rajiv, 2015. "Coalition Formation," Handbook of Game Theory with Economic Applications,, Elsevier.
    6. Mauleon, Ana & Roehl, Nils & Vannetelbosch, Vincent, 2019. "Paths to stability for overlapping group structures," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 19-24.
    7. Geoffroy de Clippel & Roberto Serrano, 2008. "Marginal Contributions and Externalities in the Value," Econometrica, Econometric Society, vol. 76(6), pages 1413-1436, November.
    8. 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.
    9. Barbera, Salvador & Gerber, Anke, 2003. "On coalition formation: durable coalition structures," Mathematical Social Sciences, Elsevier, vol. 45(2), pages 185-203, April.
    10. Kenzo Imamura & Hideo Konishi, 2023. "Assortative Matching with Externalities and Farsighted Agents," Dynamic Games and Applications, Springer, vol. 13(2), pages 497-509, June.
    11. Debraj Ray & Rajiv Vohra, 2013. "The Farsighted Stable Set," Working Papers 2013-11, Brown University, Department of Economics.
    12. Geoffroy de Clippel & Roberto Serrano, 2008. "Bargaining, coalitions and externalities: A comment on Maskin," Working Papers 2008-11, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
    13. G.-Herman Demeze-Jouatsa & Dominik Karos, 2023. "Farsighted Rationality in Hedonic Games," Dynamic Games and Applications, Springer, vol. 13(2), pages 462-479, June.
    14. Dominik Karos, 2015. "Stable partitions for games with non-transferable utilities and externalities," Economics Series Working Papers 741, University of Oxford, Department of Economics.
    15. P. Jean-Jacques Herings & Ana Mauleon & Vincent Vannetelbosch, 2010. "Coalition Formation among Farsighted Agents," Games, MDPI, vol. 1(3), pages 1-13, September.
    16. Effrosyni Diamantoudi & Licun Xue, 2003. "Farsighted stability in hedonic games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(1), pages 39-61, August.
    17. Geoffroy de Clippel & Roberto Serrano, 2008. "Bargaining, Coalitions and Externalities: a Comment on Maskin," Working Papers 2008-16, Brown University, Department of Economics.
    18. Vartiainen, Hannu, 2011. "Dynamic coalitional equilibrium," Journal of Economic Theory, Elsevier, vol. 146(2), pages 672-698, March.
    19. Dominik Karos, 2013. "Bargaining and Power," Working Papers 2013.63, Fondazione Eni Enrico Mattei.
    20. Herings, P. Jean-Jacques & Kóczy, László Á., 2021. "The equivalence of the minimal dominant set and the myopic stable set for coalition function form games," Games and Economic Behavior, Elsevier, vol. 127(C), pages 67-79.

    More about this item

    Keywords

    axiomatization; coalition formation; coalition structure; monotonicity;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:wap:wpaper:1904. 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: Haruko Noguchi (email available below). General contact details of provider: https://edirc.repec.org/data/spwasjp.html .

    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.