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Impacts of boycotts concerning the Shapley value and extensions

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  • Besner, Manfred

Abstract

If a player boycotts another player, it means that the cooperation gains of all coalitions containing both players vanish. In the associated coalition function, both players are now disjointly productive with respect to each other. The disjointly productive players property states that a player's payoff does not change when another player who is disjointly productive to that player is removed from the game. We show that the Shapley value is the only TU-value that satisfies efficiency and the disjointly productive players property and for which the impact of a boycott is the same for the boycotting and the boycotted player. Analogous considerations are made for the proportional Shapley value and the class of (positively) weighted Shapley values.

Suggested Citation

  • Besner, Manfred, 2022. "Impacts of boycotts concerning the Shapley value and extensions," MPRA Paper 112620, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:112620
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    References listed on IDEAS

    as
    1. 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.
    2. Marc Roubens & Michel Grabisch, 1999. "An axiomatic approach to the concept of interaction among players in cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 547-565.
    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. Nowak, A.S. & Radzik, T., 1995. "On axiomatizations of the weighted Shapley values," Games and Economic Behavior, Elsevier, vol. 8(2), pages 389-405.
    5. Besner, Manfred, 2022. "Disjointly productive players and the Shapley value," Games and Economic Behavior, Elsevier, vol. 133(C), pages 109-114.
    6. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    7. Manfred Besner, 2019. "Axiomatizations of the proportional Shapley value," Theory and Decision, Springer, vol. 86(2), pages 161-183, March.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Cooperative game · (Weighted/proportional) Shapley value · Disjointly productive players · (Weighted/proportional) impacts of boycotts;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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