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Marginalism, egalitarianism and efficiency in multi-choice games

Author

Listed:
  • David Lowing

    (Kyushu University)

  • Kevin Techer

    (GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne - ENS de Lyon - École normale supérieure de Lyon - Université de Lyon - UL2 - Université Lumière - Lyon 2 - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique)

Abstract

The search for a compromise between marginalism and egalitarianism has given rise to many discussions. In the context of cooperative games, this compromise can be understood as a trade-off between the Shapley value and the Equal division value. We investigate this compromise in the context of multi-choice games in which players have several activity levels. To do so, we propose new extensions of the Shapley value and of the Weighted Division values to multi-choice games. Contrary to the existing solution concepts for multi-choice games, each one of these values satisfies a core condition introduced by Grabisch and Xie (2007), namely Multi-Efficiency. We compromise between marginalism and egalitarianism by introducing the multi-choice Egalitarian Shapley values, computed as the convex combination of our extensions. To conduct this study, we introduce new axioms for multi-choice games. This allows us to provide an axiomatic foundation for each of these values.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • David Lowing & Kevin Techer, 2022. "Marginalism, egalitarianism and efficiency in multi-choice games," Post-Print hal-04097849, HAL.
    • Handle: RePEc:hal:journl:hal-04097849
    DOI: 10.1007/s00355-022-01412-8
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    Cited by:

    1. Abe, Takaaki & Lowing, David & Nakada, Satoshi, 2025. "Fair allocation in hierarchies: A compromise between marginalism and egalitarianism," Journal of Mathematical Economics, Elsevier, vol. 119(C).
    2. Lowing, David & Techer, Kevin, 2025. "Toward a consensus on extended Shapley values for multi-choice games," Mathematical Social Sciences, Elsevier, vol. 137(C).
    3. David Lowing & Makoto Yokoo, 2025. "Sharing values for multi-choice games: an axiomatic approach," International Journal of Game Theory, Springer;Game Theory Society, vol. 54(2), pages 1-32, December.
    4. Sylvain Béal & Adriana Navarro-Ramos & Eric Rémila & Philippe Solal, 2023. "Sharing the cost of hazardous transportation networks and the Priority Shapley value," Working Papers hal-04222245, HAL.
    5. Lowing, David, 2024. "Cost allocation in energy distribution networks," Journal of Mathematical Economics, Elsevier, vol. 110(C).
    6. David Lowing, 2023. "Allocation rules for multi-choice games with a permission tree structure," Annals of Operations Research, Springer, vol. 320(1), pages 261-291, January.
    7. repec:hal:wpaper:hal-04018735 is not listed on IDEAS
    8. Sylvain Béal & Adriana Navarro-Ramos & Eric Rémila & Philippe Solal, 2025. "Sharing the cost of hazardous transportation networks and the Priority Shapley value for multi-choice games," Annals of Operations Research, Springer, vol. 345(1), pages 59-103, February.
    9. Kevin Techer, 2023. "Hazardous waste transportation: a cost allocation analysis," Working Papers hal-04099139, HAL.
    10. Lowing, David & Techer, Kevin, 2022. "Priority relations and cooperation with multiple activity levels," Journal of Mathematical Economics, Elsevier, vol. 102(C).

    More about this item

    JEL classification:

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

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