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The core of bicapacities and bipolar games

Author

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  • Lijue Xie

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - 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

Bicooperative games generalize classical cooperative games in the sense that a player is allowed to play in favor or against some aim, besides non participation. Bicapacities are monotonic bicooperative games, they are useful in decision making where underlying scales are of bipolar nature, i.e., they distinguish between good/satisfactory values and bad/unsatisfactory ones. We propose here a more general framework to represent such situations, called bipolar game. We study the problem of finding the core of such games, i.e., theset of additive dominating games.

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  • Lijue Xie & Michel Grabisch, 2007. "The core of bicapacities and bipolar games," Post-Print halshs-00187162, HAL.
    • Handle: RePEc:hal:journl:halshs-00187162
    DOI: 10.1016/j.fss.2006.12.007
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00187162
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    References listed on IDEAS

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    1. 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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    Keywords

    fuzzy measure; bicapacity; cooperative game; bipolar scale; core;
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