[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/eee/ecolet/v238y2024ics016517652400168x.html
   My bibliography  Save this article

New characterizations of the Shapley value using weak differential marginalities

Author

Listed:
  • Shan, Erfang
  • Cui, Zeguang
  • Yu, Bingxin
Abstract
The principle of differential marginality for cooperative games states that the payoff differential of two players does not change whenever their productivity differential, measured by the differentials of their marginal contributions to coalitions containing neither of them, does not change. The hypothesis of differential marginality is satisfied if and only if the two players are symmetric in the difference of the two games under consideration. In this paper we introduce two weakened variants of differential marginality in which symmetric players in the difference of the two games are replaced by mutually dependent players and necessary players, respectively. By combining these weakened versions of differential marginality with the standard axioms: efficiency and either the null player out property or the disjointly productive players property, we provide two new characterizations of the Shapley value for the setting of variable player sets.

Suggested Citation

  • Shan, Erfang & Cui, Zeguang & Yu, Bingxin, 2024. "New characterizations of the Shapley value using weak differential marginalities," Economics Letters, Elsevier, vol. 238(C).
    • Handle: RePEc:eee:ecolet:v:238:y:2024:i:c:s016517652400168x
    DOI: 10.1016/j.econlet.2024.111685
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016517652400168X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.econlet.2024.111685?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. Besner, Manfred, 2022. "Disjointly productive players and the Shapley value," Games and Economic Behavior, Elsevier, vol. 133(C), pages 109-114.
    2. Casajus, André, 2018. "Symmetry, mutual dependence, and the weighted Shapley values," Journal of Economic Theory, Elsevier, vol. 178(C), pages 105-123.
    3. André Casajus, 2011. "Differential marginality, van den Brink fairness, and the Shapley value," Theory and Decision, Springer, vol. 71(2), pages 163-174, August.
    4. Casajus, André & Yokote, Koji, 2017. "Weak differential marginality and the Shapley value," Journal of Economic Theory, Elsevier, vol. 167(C), pages 274-284.
    5. Nowak, A.S. & Radzik, T., 1995. "On axiomatizations of the weighted Shapley values," Games and Economic Behavior, Elsevier, vol. 8(2), pages 389-405.
    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. Sylvain Béal & Sylvain Ferrières & Adriana Navarro‐Ramos & Philippe Solal, 2023. "Axiomatic characterizations of the family of Weighted priority values," International Journal of Economic Theory, The International Society for Economic Theory, vol. 19(4), pages 787-816, December.
    2. 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).
    3. Casajus, André, 2018. "Symmetry, mutual dependence, and the weighted Shapley values," Journal of Economic Theory, Elsevier, vol. 178(C), pages 105-123.
    4. Manfred Besner, 2020. "Value dividends, the Harsanyi set and extensions, and the proportional Harsanyi solution," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(3), pages 851-873, September.
    5. Takaaki Abe & Satoshi Nakada, 2023. "Core stability of the Shapley value for cooperative games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 60(4), pages 523-543, May.
    6. van den Brink, René & Núñez, Marina & Robles, Francisco, 2021. "Valuation monotonicity, fairness and stability in assignment problems," Journal of Economic Theory, Elsevier, vol. 195(C).
    7. Shan, Erfang & Cui, Zeguang & Lyu, Wenrong, 2023. "Gain–loss and new axiomatizations of the Shapley value," Economics Letters, Elsevier, vol. 228(C).
    8. Besner, Manfred, 2022. "The grand surplus value and repeated cooperative cross-games with coalitional collaboration," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    9. Casajus, André, 2019. "Relaxations of symmetry and the weighted Shapley values," Economics Letters, Elsevier, vol. 176(C), pages 75-78.
    10. Besner, Manfred, 2021. "Disjointly and jointly productive players and the Shapley value," MPRA Paper 108511, University Library of Munich, Germany.
    11. Takumi Kongo, 2020. "Similarities in axiomatizations: equal surplus division value and first-price auctions," Review of Economic Design, Springer;Society for Economic Design, vol. 24(3), pages 199-213, December.
    12. Kongo, Takumi, 2019. "Players’ nullification and the weighted (surplus) division values," Economics Letters, Elsevier, vol. 183(C), pages 1-1.
    13. André Casajus & Koji Yokote, 2019. "Weakly differentially monotonic solutions for cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(3), pages 979-997, September.
    14. Emilio Calvo Ramón & Esther Gutiérrez-López, 2022. "The equal collective gains value in cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(1), pages 249-278, March.
    15. C. Manuel & E. Ortega & M. del Pozo, 2023. "Marginality and the position value," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 459-474, July.
    16. Takaaki Abe & Satoshi Nakada, 2019. "The weighted-egalitarian Shapley values," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(2), pages 197-213, February.
    17. Pedro Calleja & Francesc Llerena, 2019. "Path monotonicity, consistency and axiomatizations of some weighted solutions," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(1), pages 287-310, March.
    18. Besner, Manfred, 2022. "Impacts of boycotts concerning the Shapley value and extensions," MPRA Paper 112620, University Library of Munich, Germany.
    19. Casajus, André, 2021. "Weakly balanced contributions and the weighted Shapley values," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    20. Casajus, André & Huettner, Frank, 2014. "Weakly monotonic solutions for cooperative games," Journal of Economic Theory, Elsevier, vol. 154(C), pages 162-172.

    More about this item

    Keywords

    TU-game; Shapley value; Differential marginality; Mutually dependent players; Necessary players; Disjointly productive players;
    All these keywords.

    JEL classification:

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

    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:eee:ecolet:v:238:y:2024:i:c:s016517652400168x. 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/ecolet .

    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.