IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v204y2025i1d10.1007_s10957-024-02601-4.html
   My bibliography  Save this article

Fair Profit Division

Author

Listed:
  • Ranojoy Basu

    (Indian Institute of Management Udaipur)

  • Conan Mukherjee

    (Indian Institute of Management Calcutta)

Abstract

We present a cooperative game theoretic approach to fair division of profit generated by overlapping teams of workers. We argue that unlike the standard notion of efficiency, individual shares must exhaust the sum of worths of all coalitions in this setting. We show that utilising the Shapley value through a suitably constructed characteristic function to account for this feature is unlikely to be practically acceptable. Instead, we directly use this no-wastage condition (we call it ‘extended efficiency’) to completely characterize two solutions of the fair division problem that satisfy monotonicity and symmetry.

Suggested Citation

  • Ranojoy Basu & Conan Mukherjee, 2025. "Fair Profit Division," Journal of Optimization Theory and Applications, Springer, vol. 204(1), pages 1-18, January.
    • Handle: RePEc:spr:joptap:v:204:y:2025:i:1:d:10.1007_s10957-024-02601-4
    DOI: 10.1007/s10957-024-02601-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-024-02601-4
    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/s10957-024-02601-4?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. Stéphane Gonzalez & Michel Grabisch, 2015. "Autonomous coalitions," Annals of Operations Research, Springer, vol. 235(1), pages 301-317, December.
    2. Björn Bartling & Ferdinand A. von Siemens, 2010. "Equal Sharing Rules in Partnerships," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 166(2), pages 299-320, June.
    3. Bas J. Dietzenbacher & Aleksei Y. Kondratev, 2023. "Fair and Consistent Prize Allocation in Competitions," Management Science, INFORMS, vol. 69(6), pages 3319-3339, June.
    4. Steven Huddart & Pierre Jinghong Liang, 2003. "Accounting in Partnerships," American Economic Review, American Economic Association, vol. 93(2), pages 410-414, May.
    5. van den Brink, Rene, 2007. "Null or nullifying players: The difference between the Shapley value and equal division solutions," Journal of Economic Theory, Elsevier, vol. 136(1), pages 767-775, September.
    6. Geoffroy de Clippel & Roberto Serrano, 2008. "Marginal Contributions and Externalities in the Value," Econometrica, Econometric Society, vol. 76(6), pages 1413-1436, November.
    7. Bengt Holmstrom, 1982. "Moral Hazard in Teams," Bell Journal of Economics, The RAND Corporation, vol. 13(2), pages 324-340, Autumn.
    8. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 249-297, July.
    9. Jonathan Levin & Steven Tadelis, 2005. "Profit Sharing and the Role of Professional Partnerships," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 120(1), pages 131-171.
    10. Karol Flores-Szwagrzak & Rafael Treibich, 2020. "Teamwork and Individual Productivity," Management Science, INFORMS, vol. 66(6), pages 2523-2544, June.
    11. Nowak, A.S. & Radzik, T., 1995. "On axiomatizations of the weighted Shapley values," Games and Economic Behavior, Elsevier, vol. 8(2), pages 389-405.
    12. Conan Mukherjee & Ranojoy Basu & Aftab Alam, 2020. "A measure of authorship by publications," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 41(3), pages 354-361, April.
    13. Herve Moulin, 2004. "Fair Division and Collective Welfare," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262633116, December.
    14. Huddart, Steven & Liang, Pierre Jinghong, 2005. "Profit sharing and monitoring in partnerships," Journal of Accounting and Economics, Elsevier, vol. 40(1-3), pages 153-187, December.
    15. Alchian, Armen A. & Demsetz, Harold, 1973. "The Property Right Paradigm," The Journal of Economic History, Cambridge University Press, vol. 33(1), pages 16-27, March.
    16. Casajus, André & Huettner, Frank, 2014. "Weakly monotonic solutions for cooperative games," Journal of Economic Theory, Elsevier, vol. 154(C), pages 162-172.
    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. Zhengxing Zou & René van den Brink & Yukihiko Funaki, 2024. "On weighted-egalitarian values for cooperative games," Tinbergen Institute Discussion Papers 24-021/II, Tinbergen Institute.
    2. Casajus, André & Huettner, Frank, 2014. "Weakly monotonic solutions for cooperative games," Journal of Economic Theory, Elsevier, vol. 154(C), pages 162-172.
    3. Gustavo Bergantiños & Juan D. Moreno-Ternero, 2020. "Sharing the Revenues from Broadcasting Sport Events," Management Science, INFORMS, vol. 66(6), pages 2417-2431, June.
    4. Brice Corgnet, 2010. "Team Formation and Self‐serving Biases," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 19(1), pages 117-135, March.
    5. Gill, David & Stone, Rebecca, 2015. "Desert and inequity aversion in teams," Journal of Public Economics, Elsevier, vol. 123(C), pages 42-54.
    6. Madhav V. Rajan & Stefan Reichelstein, 2006. "Subjective Performance Indicators and Discretionary Bonus Pools," Journal of Accounting Research, Wiley Blackwell, vol. 44(3), pages 585-618, June.
    7. Li, Wenzhong & Xu, Genjiu & van den Brink, René, 2024. "Sign properties and axiomatizations of the weighted division values," Journal of Mathematical Economics, Elsevier, vol. 112(C).
    8. 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.
    9. Daniel Aobdia, 2020. "The Economic Consequences of Audit Firms’ Quality Control System Deficiencies," Management Science, INFORMS, vol. 66(7), pages 2883-2905, July.
    10. Abe, Takaaki & Nakada, Satoshi, 2023. "The in-group egalitarian Owen values," Games and Economic Behavior, Elsevier, vol. 142(C), pages 1-16.
    11. Hendrik Hakenes & Svetlana Katolnik, 2018. "Optimal Team Size and Overconfidence," Group Decision and Negotiation, Springer, vol. 27(4), pages 665-687, August.
    12. Linus Wilson, 2012. "Financing professional partnerships," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 36(1), pages 58-92, January.
    13. Jürgen Ernstberger & Christopher Koch & Eva Maria Schreiber & Greg Trompeter, 2020. "Are Audit Firms' Compensation Policies Associated with Audit Quality?," Contemporary Accounting Research, John Wiley & Sons, vol. 37(1), pages 218-244, March.
    14. Vereshchagina, Galina, 2019. "The role of individual financial contributions in the formation of entrepreneurial teams," European Economic Review, Elsevier, vol. 113(C), pages 173-193.
    15. Christian Basteck & Frank Huettner, 2023. "Coalitional Manipulations and Immunity of the Shapley Value," Papers 2310.20415, arXiv.org.
    16. Bergantiños, Gustavo & Moreno-Ternero, Juan D., 2022. "Monotonicity in sharing the revenues from broadcasting sports leagues," European Journal of Operational Research, Elsevier, vol. 297(1), pages 338-346.
    17. Matthias Fahn & Hendrik Hakenes, 2019. "Teamwork as a Self-Disciplining Device," American Economic Journal: Microeconomics, American Economic Association, vol. 11(4), pages 1-32, November.
    18. Kurschilgen, Michael & Morell, Alexander & Weisel, Ori, 2017. "Internal conflict, market uniformity, and transparency in price competition between teams," Journal of Economic Behavior & Organization, Elsevier, vol. 144(C), pages 121-132.
    19. 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.).
    20. De Marco, Giuseppe & Immordino, Giovanni, 2013. "Partnership, reciprocity and team design," Research in Economics, Elsevier, vol. 67(1), pages 39-58.

    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:joptap:v:204:y:2025:i:1:d:10.1007_s10957-024-02601-4. 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.