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The Egalitarian Shapley value: a generalization based on coalition sizes

Author

Listed:
  • Dhrubajit Choudhury

    (Dibrugarh University)

  • Surajit Borkotokey

    (Dibrugarh University)

  • Rajnish Kumar

    (Queen’s University Belfast)

  • Sudipta Sarangi

    (Virginia Tech)

Abstract

In designing solution concepts for cooperative games with transferable utilities, consolidation of marginalism and egalitarianism has been widely studied. The $$\alpha $$ α -Egalitarian Shapley value is one such solution that combines the Shapley value and the Equal Division rule, the two most popular extreme instances of marginalism and egalitarianism respectively. This value gives the planner the flexibility to choose the level of marginality for the players by varying the convexity parameter $$\alpha $$ α . In this paper, we define the Generalized Egalitarian Shapley value that gives the planner more flexibility in choosing the level of marginality based on the coalition size. We then provide two characterizations of the Generalized Egalitarian Shapley value.

Suggested Citation

  • Dhrubajit Choudhury & Surajit Borkotokey & Rajnish Kumar & Sudipta Sarangi, 2021. "The Egalitarian Shapley value: a generalization based on coalition sizes," Annals of Operations Research, Springer, vol. 301(1), pages 55-63, June.
    • Handle: RePEc:spr:annopr:v:301:y:2021:i:1:d:10.1007_s10479-020-03675-9
    DOI: 10.1007/s10479-020-03675-9
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    Cited by:

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    2. Abe, Takaaki & Nakada, Satoshi, 2023. "The in-group egalitarian Owen values," Games and Economic Behavior, Elsevier, vol. 142(C), pages 1-16.
    3. Saavedra–Nieves, Alejandro & Casas–Méndez, Balbina, 2023. "On the centrality analysis of covert networks using games with externalities," European Journal of Operational Research, Elsevier, vol. 309(3), pages 1365-1378.
    4. Takumi Kongo, 2024. "Equal support from others for unproductive players: efficient and linear values that satisfy the equal treatment and weak null player out properties for cooperative games," Annals of Operations Research, Springer, vol. 338(2), pages 973-989, July.
    5. Giacomo Morelli, 2024. "Responsible investing and portfolio selection: a shapley - CVaR approach," Annals of Operations Research, Springer, vol. 342(3), pages 1991-2019, November.
    6. Gómez-Rodríguez, Marcos & Davila-Pena, Laura & Casas-Méndez, Balbina, 2024. "Cost allocation problems on highways with grouped users," European Journal of Operational Research, Elsevier, vol. 316(2), pages 667-679.
    7. Jun Su & Yuan Liang & Guangmin Wang & Genjiu Xu, 2020. "Characterizations, Potential, and an Implementation of the Shapley-Solidarity Value," Mathematics, MDPI, vol. 8(11), pages 1-20, November.
    8. Surajit Borkotokey & Sujata Goala & Niharika Kakoty & Parishmita Boruah, 2022. "The component-wise egalitarian Myerson value for Network Games," Papers 2201.02793, arXiv.org.
    9. Ghislain Herman Demeze-Jouatsa & Roland Pongou & Jean-Baptiste Tondji, 2024. "Justice, inclusion, and incentives," Journal of Theoretical Politics, , vol. 36(2), pages 101-131, April.

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    More about this item

    Keywords

    Shapley value; Equal division rule; Solidarity; Egalitarian Shapley value;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D60 - Microeconomics - - Welfare Economics - - - General

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