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A value for bi-cooperative games

Author

Listed:
  • Christophe Labreuche

    () (UMP CNRS/THALES - Unité mixte de physique CNRS/Thalès - THALES - CNRS - Centre National de la Recherche Scientifique)

  • Michel Grabisch

    () (CES - Centre d'économie de la Sorbonne - CNRS - Centre National de la Recherche Scientifique - UP1 - Université Panthéon-Sorbonne)

Abstract

Bi-cooperative games were introduced by Bilbao et al. as a generalization of TU cooperative games, in which each player can participate positively, negatively, or not at all. In this paper, we propose a definition of a share of the worth obtained by some players after they decided on their participation in the game. It turns out that the cost allocation rule does not look for a given player to her contribution at the opposite participation option to the one she chooses. The relevance of the value is discussed on several examples.

Suggested Citation

  • Christophe Labreuche & Michel Grabisch, 2008. "A value for bi-cooperative games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00308738, HAL.
  • Handle: RePEc:hal:cesptp:halshs-00308738
    DOI: 10.1007/s00182-008-0126-5
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00308738
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    File URL: https://halshs.archives-ouvertes.fr/halshs-00308738/document
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    References listed on IDEAS

    as
    1. Christophe Labreuche & Michel Grabisch, 2006. "Axiomatisation of the Shapley value and power index for bi-cooperative games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00113340, HAL.
    2. Labreuche, Christophe & Grabisch, Michel, 2006. "Generalized Choquet-like aggregation functions for handling bipolar scales," European Journal of Operational Research, Elsevier, vol. 172(3), pages 931-955, August.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Michel Grabisch & Christophe Labreuche, 2010. "A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid," Annals of Operations Research, Springer, vol. 175(1), pages 247-286, March.
    2. Michel Grabisch, 2010. "Ensuring the boundedness of the core of games with restricted cooperation," Post-Print halshs-00544134, HAL.
    3. Ulrich Faigle & Michel Grabisch, 2017. "Game Theoretic Interaction and Decision: A Quantum Analysis," Games, MDPI, Open Access Journal, vol. 8(4), pages 1-25, November.
    4. Michel Grabisch, 2011. "Ensuring the boundedness of the core of games with restricted cooperation," Annals of Operations Research, Springer, vol. 191(1), pages 137-154, November.

    More about this item

    Keywords

    Bi-cooperative games; Efficiency; Value;

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