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A value for bi-cooperative games

Author

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  • Christophe Labreuche

    (Laboratoire Albert Fert (ex-UMPhy Unité mixte de physique CNRS/Thales) - THALES [France] - Université Paris-Saclay - CNRS - Centre National de la Recherche Scientifique)

  • Michel Grabisch

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

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://shs.hal.science/halshs-00308738
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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. Dominique Henriet & Herve' Moulin, 1996. "Traffic-Based Cost Allocation in a Network," RAND Journal of Economics, The RAND Corporation, vol. 27(2), pages 332-345, Summer.
    3. 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.
    4. Sergiu Hart, 2006. "Shapley Value," Discussion Paper Series dp421, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    5. Michel Grabisch, 2006. "Aggregation on bipolar scales," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00187155, HAL.
    6. Sprumont, Yves, 2000. "Coherent Cost-Sharing Rules," Games and Economic Behavior, Elsevier, vol. 33(1), pages 126-144, October.
    7. Hsiao Chih-Ru & Raghavan T. E. S., 1993. "Shapley Value for Multichoice Cooperative Games, I," Games and Economic Behavior, Elsevier, vol. 5(2), pages 240-256, April.
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    Cited by:

    1. Ulrich Faigle & Michel Grabisch, 2017. "Game Theoretic Interaction and Decision: A Quantum Analysis," Games, MDPI, vol. 8(4), pages 1-25, November.
    2. 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.
    3. 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.

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