IDEAS home Printed from https://ideas.repec.org/p/bge/wpaper/1427.html
   My bibliography  Save this paper

Sequential Creation of Surplus and the Shapley Value

Author

Listed:
  • Mikel à lvarez-Mozos
  • David Pérez-Castrillo
  • Inés Macho-Stadler

Abstract

We introduce the family of games with intertemporal externalities, where two disjoint sets of players play sequentially. Coalitions formed by the present cohort generate worth today. Moreover, today's partition of players exerts an externality on the future; the worth of a coalition formed by future players is influenced by this externality. We adapt the classic Shapley axioms and study their implications in our class of games. They do not suffice to single out a unique solution. We introduce two values using the interpretation of the Shapley value as the players' expected contributions to coalitions: the one-coalition externality value and the naive value. We state a relationship between these values and the Shapley value of an associated game in characteristic function form. Our main results characterize the two values by adding one additional property to the classic Shapley axioms. A property of equal treatment of contributions leads to characterizing the one-coalition externality value. A property of equal treatment of externalities characterizes the naive value

Suggested Citation

  • Mikel à lvarez-Mozos & David Pérez-Castrillo & Inés Macho-Stadler, 2024. "Sequential Creation of Surplus and the Shapley Value," Working Papers 1427, Barcelona School of Economics.
    • Handle: RePEc:bge:wpaper:1427
    as

    Download full text from publisher

    File URL: https://bw.bse.eu/wp-content/uploads/2024/02/1427-file.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Bolger, E M, 1989. "A Set of Axioms for a Value for Partition Function Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(1), pages 37-44.
    2. McQuillin, Ben, 2009. "The extended and generalized Shapley value: Simultaneous consideration of coalitional externalities and coalitional structure," Journal of Economic Theory, Elsevier, vol. 144(2), pages 696-721, March.
    3. Effrosyni Diamantoudi & Inés Macho-Stadler & David Pérez-Castrillo & Licun Xue, 2015. "Sharing the surplus in games with externalities within and across issues," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(2), pages 315-343, 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. Ander Perez-Orive & Andrea Caggese, 2017. "Capital Misallocation and Secular Stagnation," 2017 Meeting Papers 382, Society for Economic Dynamics.
    2. 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.
    3. 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.
    4. Messan Agbaglah, 2017. "Overlapping coalitions, bargaining and networks," Theory and Decision, Springer, vol. 82(3), pages 435-459, March.
    5. 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.
    6. Casajus, André & Funaki, Yukihiko & Huettner, Frank, 2024. "Random partitions, potential, value, and externalities," Games and Economic Behavior, Elsevier, vol. 147(C), pages 88-106.
    7. Inés Macho-Stadler & David Pérez-Castrillo & David Wettstein, 2008. "Dividends and Weighted Values in Games with Externalities," Working Papers 366, Barcelona School of Economics.
    8. Funaki, Yukihiko & Núñez, Marina, 2024. "Some advances in cooperative game theory: Indivisibilities, externalities and axiomatic approach," Journal of Mathematical Economics, Elsevier, vol. 115(C).
    9. Effrosyni Diamantoudi & Inés Macho-Stadler & David Pérez-Castrillo & Licun Xue, 2015. "Sharing the surplus in games with externalities within and across issues," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(2), pages 315-343, October.
    10. Roger A McCain, 2013. "Value Solutions in Cooperative Games," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8528.
    11. Oskar Skibski & Tomasz Michalak, 2020. "Fair division in the presence of externalities," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(1), pages 147-172, March.
    12. Justin Chan, 2024. "Implementations of Cooperative Games Under Non-Cooperative Solution Concepts," Papers 2402.14952, arXiv.org, revised Apr 2024.
    13. Andr'e Casajus & Yukihiko Funaki & Frank Huettner, 2024. "Random partitions, potential, value, and externalities," Papers 2402.00394, arXiv.org, revised Jun 2024.
    14. Macho-Stadler, Inés & Pérez-Castrillo, David & Wettstein, David, 2018. "Values for environments with externalities – The average approach," Games and Economic Behavior, Elsevier, vol. 108(C), pages 49-64.
    15. M. Josune Albizuri & Satoshi Masuya & José M. Zarzuelo, 2024. "Values for Restricted Games with Externalities," Group Decision and Negotiation, Springer, vol. 33(2), pages 351-369, April.
    16. 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.
    17. László Á. Kóczy, 2018. "Partition Function Form Games," Theory and Decision Library C, Springer, number 978-3-319-69841-0, September.
    18. Skibski, Oskar & Michalak, Tomasz P. & Wooldridge, Michael, 2018. "The Stochastic Shapley Value for coalitional games with externalities," Games and Economic Behavior, Elsevier, vol. 108(C), pages 65-80.
    19. Julio Rodríguez-Segura & Joss Sánchez-Pérez, 2017. "An Extension of the Solidarity Value for Environments with Externalities," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(02), pages 1-12, June.
    20. 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.

    More about this item

    Keywords

    ;
    ;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D62 - Microeconomics - - Welfare Economics - - - Externalities

    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:bge:wpaper:1427. 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: Bruno Guallar (email available below). General contact details of provider: https://edirc.repec.org/data/bargses.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.