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Cooperative games with unpaid players

Author

Listed:
  • Sylvain Béal

    (Université Marie et Louis Pasteur, CRESE UR3190, F-25000 Besançon, France)

  • Léa Munich

    (Université Paris Panthéon Assas, CRED UR 7321, F-75005 Paris, France)

  • Philippe Solal

    (Université de Saint-Etienne, GATE Lyon Saint-Etienne, UMR 5824, F-42023 Saint-Etienne, France)

  • Kevin Techer

    (Université Marie et Louis Pasteur, CRESE UR3190, F-25000 Besançon, France)

Abstract

We consider cooperative TU-games with unpaid players, which are described by a TUgame and two categories of players, paid and unpaid. Unpaid players participate in the cooperative game but are not rewarded for their participation, for instance for legal reasons. The objective is then to determine how the contributions of unpaid players are redistributed among the paid players. To meet this goal, we introduce and characterize axiomatically three values that are inspired by the Shapley value but differ in the way they redistribute the contributions of unpaid players. These values are unified as instances of a more general two-step allocation procedure.

Suggested Citation

  • Sylvain Béal & Léa Munich & Philippe Solal & Kevin Techer, 2025. "Cooperative games with unpaid players," Working Papers 2025-11, CRESE.
    • Handle: RePEc:crb:wpaper:2025-11
    as

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    References listed on IDEAS

    as
    1. Hougaard, Jens Leth & Moreno-Ternero, Juan D. & Østerdal, Lars Peter, 2012. "A unifying framework for the problem of adjudicating conflicting claims," Journal of Mathematical Economics, Elsevier, vol. 48(2), pages 107-114.
    2. Yuan Ju & Peter Borm & Pieter Ruys, 2007. "The consensus value: a new solution concept for cooperative games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(4), pages 685-703, June.
    3. Sylvain Béal & Sylvain Ferrières & Philippe Solal, 2022. "The priority value for cooperative games with a priority structure," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(2), pages 431-450, June.
    4. Casajus, André & Huettner, Frank, 2014. "Weakly monotonic solutions for cooperative games," Journal of Economic Theory, Elsevier, vol. 154(C), pages 162-172.
    5. William Thomson, 2011. "Consistency and its converse: an introduction," Review of Economic Design, Springer;Society for Economic Design, vol. 15(4), pages 257-291, December.
    6. Chun, Youngsub, 1989. "A new axiomatization of the shapley value," Games and Economic Behavior, Elsevier, vol. 1(2), pages 119-130, June.
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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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