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The weighted Shapley-egalitarian value for cooperative games with a coalition structure

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  • Xun-Feng Hu

    (Guangzhou University)

Abstract

In this paper, we study a solution, the weighted Shapley-egalitarian value, for transferable utility cooperative games with a coalition structure. It first distributes the worth of the grand coalition among a priori unions of the coalition structure with the weighted Shapley value, with the sizes of unions acting as weights. And then, it allocates the payoff of every union among its players with the equal division value, thus players inside a union exhibit a greater degree of solidarity than players in different unions. We give several equivalent definitions of the value, particularly show its relationship with the collective value. We apply the value to the recent field of airport cost pooling game, and find that the Shapley value therein can be viewed as a special case of our value, if we view an airport cost pooling game as a transferable utility cooperative game with a coalition structure. Finally, to further highlight the differences between our value and the collective value, we provide parallel axiomatizations of the two values, by replacing the collective balanced contributions axiom with two intuitive axioms.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:topjnl:v:28:y:2020:i:1:d:10.1007_s11750-019-00530-4
    DOI: 10.1007/s11750-019-00530-4
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    Cited by:

    1. Jilei Shi & Lei Cai & Erfang Shan & Wenrong Lyu, 2022. "A value for cooperative games with coalition and probabilistic graph structures," Journal of Combinatorial Optimization, Springer, vol. 43(3), pages 646-671, April.
    2. Xun-Feng Hu, 2021. "New axiomatizations of the Owen value," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(3), pages 585-603, June.
    3. 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.
    4. 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.
    5. 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.

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    More about this item

    Keywords

    Cooperative game; Coalition structure; Shapley-solidarity value; Collective value; Airport cost pooling game;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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