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Coalitional substitution of players and the proportional Shapley value

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  • Besner, Manfred

Abstract

We present a new axiomatization of the proportional Shapley Value. Our study is based on three axioms: efficiency, which ensures that the total worth of the grand coalition is fully distributed among the players; the disjointly productive players property, which states that removing a player who has no cooperative interactions with another player does not affect that player's payoff; and a new axiom that makes the difference to the classical Shapley value. This axiom, the coalitional substitution of players property, involves a scenario in which a player's cooperative contribution to a coalition is replaced by that of a group of new players whose combined individual worths match that of the original player. The key point is that the payoffs to the remaining players remain unaffected.

Suggested Citation

  • Besner, Manfred, 2025. "Coalitional substitution of players and the proportional Shapley value," MPRA Paper 123720, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:123720
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    File URL: https://mpra.ub.uni-muenchen.de/123965/1/MPRA_paper_123965.pdf
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    References listed on IDEAS

    as
    1. Billot, Antoine & Thisse, Jacques-Francois, 2005. "How to share when context matters: The Mobius value as a generalized solution for cooperative games," Journal of Mathematical Economics, Elsevier, vol. 41(8), pages 1007-1029, December.
    2. Besner, Manfred, 2022. "Impacts of boycotts concerning the Shapley value and extensions," MPRA Paper 112620, University Library of Munich, Germany.
    3. Béal, Sylvain & Ferrières, Sylvain & Rémila, Eric & Solal, Philippe, 2018. "The proportional Shapley value and applications," Games and Economic Behavior, Elsevier, vol. 108(C), pages 93-112.
    4. Zhengxing Zou & René Brink & Youngsub Chun & Yukihiko Funaki, 2021. "Axiomatizations of the proportional division value," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(1), pages 35-62, July.
    5. Besner, Manfred, 2022. "Disjointly productive players and the Shapley value," Games and Economic Behavior, Elsevier, vol. 133(C), pages 109-114.
    6. Besner, Manfred, 2022. "Impacts of boycotts concerning the Shapley value and extensions," Economics Letters, Elsevier, vol. 217(C).
    7. André Casajus & Rodrigue Tido Takeng, 2024. "Second-order productivity, second-order payoffs, and the Banzhaf value," Post-Print hal-04574752, HAL.
    8. André Casajus & Rodrigue Tido Takeng, 2024. "Second-order productivity, second-order payoffs, and the Banzhaf value," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(3), pages 989-1004, September.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Cooperative game; Proportional Shapley value; Disjointly productive players; Coalitional substitution of players; Patronage refunds;
    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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