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Disjointly productive players and the Shapley value

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  • Besner, Manfred

Abstract

Central to this note is the concept of disjointly productive players. Two players are disjointly productive if there is no synergy effect if one of these players joins a coalition containing the other. Our first new axiom states that the payoff to a player does not change when another player, disjointly productive in relation to that player, leaves the game. The second new axiom implies that if a player splits into two disjointly productive players who together contribute the same to the game as the original player, the payoff to another player does not change. These two axioms, along with efficiency, characterize the Shapley value.

Suggested Citation

  • Besner, Manfred, 2022. "Disjointly productive players and the Shapley value," Games and Economic Behavior, Elsevier, vol. 133(C), pages 109-114.
    • Handle: RePEc:eee:gamebe:v:133:y:2022:i:c:p:109-114
    DOI: 10.1016/j.geb.2022.03.002
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    References listed on IDEAS

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    1. Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(2), pages 89-99.
    2. 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.
    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. 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.
    5. Manfred Besner, 2019. "Axiomatizations of the proportional Shapley value," Theory and Decision, Springer, vol. 86(2), pages 161-183, March.
    6. Nowak, A.S. & Radzik, T., 1995. "On axiomatizations of the weighted Shapley values," Games and Economic Behavior, Elsevier, vol. 8(2), pages 389-405.
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    Citations

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    Cited by:

    1. Besner, Manfred, 2022. "Impacts of boycotts concerning the Shapley value and extensions," MPRA Paper 112620, University Library of Munich, Germany.
    2. Sylvain Béal & Marc Deschamps & Alexandre Skoda, 2024. "The neighborhood value for cooperative graph games," Working Papers 2024-16, CRESE.
    3. Shan, Erfang & Cui, Zeguang & Yu, Bingxin, 2024. "New characterizations of the Shapley value using weak differential marginalities," Economics Letters, Elsevier, vol. 238(C).
    4. Besner, Manfred, 2022. "Impacts of boycotts concerning the Shapley value and extensions," Economics Letters, Elsevier, vol. 217(C).

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