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Associated consistency and the Aumann-Drèze value

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  • Florian Navarro

    (GRANEM - Groupe de Recherche Angevin en Economie et Management - UA - Université d'Angers - Institut Agro Rennes Angers - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement)

Abstract

This article presents an axiomatic characterization of the Aumann-Drèze value (1974) for cooperative games with coalition structures. We build an associated game that extends the original associated game presented by Hamiache (2001) to cooperative games with coalition structures. We use a similar approach to the one used in Hamiache and Navarro (2020). This new associated game is expressed through a matrix form. We show that the series of successive associated games is convergent and that its limit is an inessential game. This allows us to propose a characterization of the Aumann-Drèze value that relies on associated consistency, inessential game and continuity axioms. Hence, this paper strengthens the results of Hamiache (2001) and Hamiache and Navarro (2020) considering that if these axioms are viewed as desirable, we are now able to provide a unique value for three different types of problems : the Shapley value on standard games (Hamiache 2001), the Hamiache-Navarro value on games with graphs (Hamiache and Navarro 2020) and the Aumann-Drèze value for games with coalition structures.

Suggested Citation

  • Florian Navarro, 2022. "Associated consistency and the Aumann-Drèze value," Post-Print hal-03678064, HAL.
    • Handle: RePEc:hal:journl:hal-03678064
    DOI: 10.1142/S0219198922500189
    Note: View the original document on HAL open archive server: https://univ-angers.hal.science/hal-03678064
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    References listed on IDEAS

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    1. Hamiache, Gerard, 1999. "A Value with Incomplete Communication," Games and Economic Behavior, Elsevier, vol. 26(1), pages 59-78, January.
    2. Gérard Hamiache, 2001. "Associated consistency and Shapley value," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 279-289.
    3. AUMANN, Robert J. & DREZE, Jacques H., 1974. "Cooperative games with coalition structures," LIDAM Reprints CORE 217, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Gérard Hamiache, 2012. "A Matrix Approach to TU Games with Coalition and Communication Structures," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(1), pages 85-100, January.
    5. Navarro, Florian, 2020. "The center value: A sharing rule for cooperative games on acyclic graphs," Mathematical Social Sciences, Elsevier, vol. 105(C), pages 1-13.
    6. Gérard Hamiache, 2004. "A mean value for games with communication structures," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(4), pages 533-544, August.
    7. Gérard Hamiache, 2010. "A Matrix Approach To The Associated Consistency With An Application To The Shapley Value," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 12(02), pages 175-187.
    8. Gérard Hamiache & Florian Navarro, 2020. "Associated consistency, value and graphs," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(1), pages 227-249, March.
    9. Yan-An Hwang, 2006. "Associated consistency and equal allocation of nonseparable costs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(3), pages 709-719, August.
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