IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v128y2024icp10-15.html
   My bibliography  Save this article

Externalities and the (pre)nucleolus in cooperative games

Author

Listed:
  • Álvarez-Mozos, Mikel
  • Ehlers, Lars

Abstract

In most economic applications of cooperative games, externalities prevail: the worth of a coalition depends on how the other players are organized. We show that there is a unique natural way of extending the prenucleolus to games with coalitional externalities. This is in contrast to the Shapley value and the core for which many different extensions have been proposed.

Suggested Citation

  • Álvarez-Mozos, Mikel & Ehlers, Lars, 2024. "Externalities and the (pre)nucleolus in cooperative games," Mathematical Social Sciences, Elsevier, vol. 128(C), pages 10-15.
    • Handle: RePEc:eee:matsoc:v:128:y:2024:i:c:p:10-15
    DOI: 10.1016/j.mathsocsci.2024.01.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016548962400012X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.mathsocsci.2024.01.003?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. Geoffroy de Clippel & Roberto Serrano, 2008. "Marginal Contributions and Externalities in the Value," Econometrica, Econometric Society, vol. 76(6), pages 1413-1436, November.
    2. László Kóczy, 2007. "A recursive core for partition function form games," Theory and Decision, Springer, vol. 63(1), pages 41-51, August.
    3. 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).
    4. Bloch, Francis & van den Nouweland, Anne, 2014. "Expectation formation rules and the core of partition function games," Games and Economic Behavior, Elsevier, vol. 88(C), pages 339-353.
    5. Frank Huettner & André Casajus, 2019. "Marginality, dividends, and the value in games with externalities," ESMT Research Working Papers ESMT-19-01, ESMT European School of Management and Technology.
    6. Inés Macho-Stadler & David Pérez-Castrillo & David Wettstein, 2010. "Dividends and weighted values in games with externalities," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 177-184, March.
    7. Dutta, Bhaskar & Ehlers, Lars & Kar, Anirban, 2010. "Externalities, potential, value and consistency," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2380-2411, November.
    8. Chris Snijders, 1995. "Axiomatization of the Nucleolus," Mathematics of Operations Research, INFORMS, vol. 20(1), pages 189-196, February.
    9. Orshan, Gooni, 1993. "The Prenucleolus and the Reduced Game Property: Equal Treatment Replaces Anonymity," International Journal of Game Theory, Springer;Game Theory Society, vol. 22(3), pages 241-248.
    10. Morton Davis & Michael Maschler, 1965. "The kernel of a cooperative game," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 12(3), pages 223-259, September.
    11. Macho-Stadler, Ines & Perez-Castrillo, David & Wettstein, David, 2007. "Sharing the surplus: An extension of the Shapley value for environments with externalities," Journal of Economic Theory, Elsevier, vol. 135(1), pages 339-356, July.
    12. J. M. Alonso-Meijide & M. Álvarez-Mozos & M. G. Fiestras-Janeiro & A. Jiménez-Losada, 2022. "On convexity in cooperative games with externalities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(1), pages 265-292, July.
    13. Hafalir, Isa E., 2007. "Efficiency in coalition games with externalities," Games and Economic Behavior, Elsevier, vol. 61(2), pages 242-258, November.
    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. Wu, Dongge & Chang, Xinyue & Xue, Yixun & Huang, Yuxi & Su, Jia & Sun, Hongbin, 2024. "Bilevel low-carbon coordinated operation of integrated energy systems considering dynamic tiered carbon pricing methodology," Energy, Elsevier, vol. 310(C).

    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. László Á. Kóczy, 2018. "Partition Function Form Games," Theory and Decision Library C, Springer, number 978-3-319-69841-0, December.
    2. Takaaki Abe, 2020. "Population monotonic allocation schemes for games with externalities," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(1), pages 97-117, March.
    3. Mikel ÁLVAREZ-MOZOS & Lars EHLERS, 2017. "Externalities and the Nucleolus," Cahiers de recherche 08-2017, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    4. Bloch, Francis & van den Nouweland, Anne, 2014. "Expectation formation rules and the core of partition function games," Games and Economic Behavior, Elsevier, vol. 88(C), pages 339-353.
    5. Maria Montero, 2023. "Coalition Formation in Games with Externalities," Dynamic Games and Applications, Springer, vol. 13(2), pages 525-548, June.
    6. J. M. Alonso-Meijide & M. Álvarez-Mozos & M. G. Fiestras-Janeiro & A. Jiménez-Losada, 2022. "On convexity in cooperative games with externalities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(1), pages 265-292, July.
    7. M. Álvarez-Mozos & O. Tejada, 2015. "The Banzhaf value in the presence of externalities," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(4), pages 781-805, April.
    8. Andrea Caggese & Ander Pérez-Orive, 2017. "Capital Misallocation and Secular Stagnation," Finance and Economics Discussion Series 2017-009, Board of Governors of the Federal Reserve System (U.S.).
    9. J. M. Alonso-Meijide & M. Álvarez-Mozos & M. G. Fiestras-Janeiro & A. Jiménez-Losada, 2021. "Marginality and convexity in partition function form games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(1), pages 99-121, August.
    10. René Brink & Dinko Dimitrov & Agnieszka Rusinowska, 2021. "Winning coalitions in plurality voting democracies," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(3), pages 509-530, April.
    11. David Wettstein & David Pérez-Castrillo & Inés Macho-Stadler, 2017. "Extensions of the Shapley value for Environments with Externalities," Working Papers 1002, Barcelona School of Economics.
    12. 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.
    13. Takaaki Abe & Yukihiko Funaki, 2017. "The non-emptiness of the core of a partition function form game," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(3), pages 715-736, August.
    14. José María Alonso-Meijide & Mikel Álvarez-Mozos & María Gloria Fiestras-Janeiro, 2015. "Power Indices and Minimal Winning Coalitions in Simple Games with Externalities Abstract: We propose a generalization of simple games to situations with coalitional externalities. The main novelty of ," UB School of Economics Working Papers 2015/328, University of Barcelona School of Economics.
    15. Takaaki Abe, 2018. "Consistency and the core in games with externalities," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(1), pages 133-154, March.
    16. Dutta, Bhaskar & Ehlers, Lars & Kar, Anirban, 2010. "Externalities, potential, value and consistency," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2380-2411, November.
    17. Geoffroy de Clippel & Roberto Serrano, 2008. "Marginal Contributions and Externalities in the Value," Econometrica, Econometric Society, vol. 76(6), pages 1413-1436, November.
    18. Messan Agbaglah, 2017. "Overlapping coalitions, bargaining and networks," Theory and Decision, Springer, vol. 82(3), pages 435-459, March.
    19. Álvarez-Mozos, M. & Alonso-Meijide, J.M. & Fiestras-Janeiro, M.G., 2017. "On the externality-free Shapley–Shubik index," Games and Economic Behavior, Elsevier, vol. 105(C), pages 148-154.
    20. Messan Agbaglah, 2014. "A recursive core for cooperative games with overlapping coalitions," Cahiers de recherche 14-07, Departement d'économique de l'École de gestion à l'Université de Sherbrooke.

    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:128:y:2024:i:c:p:10-15. 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.