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Associated consistency, value and graphs

Author

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  • Gérard Hamiache

    (EQUIPPE - Economie Quantitative, Intégration, Politiques Publiques et Econométrie - Université de Lille, Sciences et Technologies - Université de Lille, Sciences Humaines et Sociales - PRES Université Lille Nord de France - Université de Lille, Droit et Santé, LEM - Lille économie management - UMR 9221 - UA - Université d'Artois - UCL - Université catholique de Lille - Université de Lille - CNRS - Centre National de la Recherche Scientifique)

  • Florian Navarro

Abstract

This article presents an axiomatic characterization of a new value for cooperative games with incomplete communication. The result is obtained by slight modifications of associated games proposed by Hamiache (Games Econ Behav 26:59–78, 1999; Int J Game Theory 30:279–289, 2001). This new associated game can be expressed as a matrix formula. We generate a series of successive associated games and show that its limit is an inessential game. Three axioms (associated consistency, inessential game, continuity) characterize a unique sharing rule. Combinatorial arguments and matrix tools provide a procedure to compute the solution. The new sharing rule coincides with the Shapley value when the communication is complete.

Suggested Citation

  • Gérard Hamiache & Florian Navarro, 2019. "Associated consistency, value and graphs," Post-Print hal-02501125, HAL.
    • Handle: RePEc:hal:journl:hal-02501125
    DOI: 10.1007/s00182-019-00688-y
    Note: View the original document on HAL open archive server: https://hal.science/hal-02501125
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    References listed on IDEAS

    as
    1. Hamiache, Gerard, 1999. "A Value with Incomplete Communication," Games and Economic Behavior, Elsevier, vol. 26(1), pages 59-78, January.
    2. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    3. Gérard Hamiache, 2001. "Associated consistency and Shapley value," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 279-289.
    4. Herings, P.J.J. & van der Laan, G. & Talman, A.J.J., 2008. "The average tree solution for cycle-free graph games," Other publications TiSEM f243609c-2847-415f-ae52-1, Tilburg University, School of Economics and Management.
    5. 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.
    6. 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.
    7. Borm, P.E.M. & Owen, G. & Tijs, S.H., 1992. "On the position value for communication situations," Other publications TiSEM 5a8473e4-1df7-42df-ad53-f, Tilburg University, School of Economics and Management.
    8. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    9. Herings, P. Jean Jacques & van der Laan, Gerard & Talman, Dolf, 2008. "The average tree solution for cycle-free graph games," Games and Economic Behavior, Elsevier, vol. 62(1), pages 77-92, January.
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    Cited by:

    1. 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.
    2. Florian Navarro, 2025. "Cooperative games with types, outside options, and the egalitarian value," Post-Print hal-04324424, HAL.
    3. Florian Navarro, 2022. "Associated consistency and the Aumann-Drèze value," Post-Print hal-03678064, HAL.
    4. Florian Navarro, 2022. "Associated consistency and the Aumann-Drèze value," Working Papers hal-03678064, HAL.

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    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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