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Two-step Shapley-solidarity value for cooperative games with coalition structure

Author

Listed:
  • Rong Zou

    (Northwestern Polytechnical University
    University of Twente)

  • Wenzhong Li

    (Northwestern Polytechnical University)

  • Marc Uetz

    (University of Twente)

  • Genjiu Xu

    (Northwestern Polytechnical University)

Abstract

This paper proposes an alternative for the two-step Shapley value for cooperative games with coalition structure that has earlier been proposed by Kamijo. The value is based on the idea that within a union of players, worth should be distributed based on the solidarity principle. Specifically, we propose a two-step Shapley-solidarity value, in which the surplus of a union’s Shapley value in the quotient game is distributed equally among the union’s members, and players obtain the solidarity value of the respective subgame within their union. We provide an intuitive procedural characterization for this value and give three axiomatizations to pinpoint the differences to comparable values.

Suggested Citation

  • Rong Zou & Wenzhong Li & Marc Uetz & Genjiu Xu, 2023. "Two-step Shapley-solidarity value for cooperative games with coalition structure," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 45(1), pages 1-25, March.
    • Handle: RePEc:spr:orspec:v:45:y:2023:i:1:d:10.1007_s00291-022-00694-9
    DOI: 10.1007/s00291-022-00694-9
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    References listed on IDEAS

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    1. Yoshio Kamijo, 2013. "The collective value: a new solution for games with coalition structures," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 572-589, October.
    2. Sylvain Béal & Eric Rémila & Philippe Solal, 2017. "Axiomatization and implementation of a class of solidarity values for TU-games," Theory and Decision, Springer, vol. 83(1), pages 61-94, June.
    3. René Brink & Yukihiko Funaki, 2015. "Implementation and axiomatization of discounted Shapley values," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(2), pages 329-344, September.
    4. Rong Zou & Genjiu Xu & Wenzhong Li & Xunfeng Hu, 2020. "A coalitional compromised solution for cooperative games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(4), pages 735-758, December.
    5. Calvo, Emilio & Javier Lasaga, J. & Winter, Eyal, 1996. "The principle of balanced contributions and hierarchies of cooperation," Mathematical Social Sciences, Elsevier, vol. 31(3), pages 171-182, June.
    6. Casas-Mendez, Balbina & Garcia-Jurado, Ignacio & van den Nouweland, Anne & Vazquez-Brage, Margarita, 2003. "An extension of the [tau]-value to games with coalition structures," European Journal of Operational Research, Elsevier, vol. 148(3), pages 494-513, August.
    7. Calvo, Emilio & Gutiérrez, Esther, 2010. "Solidarity in games with a coalition structure," Mathematical Social Sciences, Elsevier, vol. 60(3), pages 196-203, November.
    8. Borkotokey, Surajit & Choudhury, Dhrubajit & Gogoi, Loyimee & Kumar, Rajnish, 2020. "Group contributions in TU-games: A class of k-lateral Shapley values," European Journal of Operational Research, Elsevier, vol. 286(2), pages 637-648.
    9. Xun-Feng Hu, 2020. "The weighted Shapley-egalitarian value for cooperative games with a coalition structure," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 193-212, April.
    10. J. M. Alonso-Meijide & J. Costa & I. García-Jurado & J. C. Gonçalves-Dosantos, 2020. "On egalitarian values for cooperative games with a priori unions," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 672-688, October.
    11. Nowak, Andrzej S & Radzik, Tadeusz, 1994. "A Solidarity Value for n-Person Transferable Utility Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(1), pages 43-48.
    12. Sprumont, Yves, 1990. "Population monotonic allocation schemes for cooperative games with transferable utility," Games and Economic Behavior, Elsevier, vol. 2(4), pages 378-394, December.
    13. 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).
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    Cited by:

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    More about this item

    Keywords

    Cooperative games; Coalition structure; Solidarity; Procedural characterization; Axiomatization;
    All these keywords.

    JEL classification:

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

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