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A coalition formation value for games with externalities

Author

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  • Michel Grabisch

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Yukihiko Funaki

    (Waseda University [Tokyo, Japan])

Abstract

The coalition formation problem in an economy with externalities can be adequately modeled by using games in partition function form (PFF games), proposed by Thrall and Lucas. If we suppose that forming the grand coalition generates the largest total surplus, a central question is how to allocate the worth of the grand coalition to each player, i.e., how to find an adequate solution concept, taking into account the whole process of coalition formation. We propose in this paper the original concepts of scenario-value, process-value and coalition formation value, which represent the average contribution of players in a scenario (a particular sequence of coalitions within a given coalition formation process), in a process (a sequence of partitions of the society), and in the whole (all processes being taken into account), respectively. We give an application to Cournot oligopoly, and two axiomatizations of the scenario-value.

Suggested Citation

  • Michel Grabisch & Yukihiko Funaki, 2011. "A coalition formation value for games with externalities," Post-Print halshs-00344797, HAL.
    • Handle: RePEc:hal:journl:halshs-00344797
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00344797v2
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    References listed on IDEAS

    as
    1. M. J. Albizuri & J. Arin & J. Rubio, 2005. "An Axiom System For A Value For Games In Partition Function Form," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 63-72.
    2. Bloch, Francis, 1996. "Sequential Formation of Coalitions in Games with Externalities and Fixed Payoff Division," Games and Economic Behavior, Elsevier, vol. 14(1), pages 90-123, May.
    3. Bolger, E M, 1989. "A Set of Axioms for a Value for Partition Function Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(1), pages 37-44.
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    Cited by:

    1. Eyckmans, Johan & Finus, Michael & Mallozzi, Lina, 2011. "A New Class of Welfare Maximizing Stable Sharing Rules for Partition Function Games with Externalities," Working Papers 2011/08, Hogeschool-Universiteit Brussel, Faculteit Economie en Management.
    2. Skibski, Oskar & Michalak, Tomasz P. & Wooldridge, Michael, 2018. "The Stochastic Shapley Value for coalitional games with externalities," Games and Economic Behavior, Elsevier, vol. 108(C), pages 65-80.
    3. Julio Rodríguez-Segura & Joss Sánchez-Pérez, 2017. "An Extension of the Solidarity Value for Environments with Externalities," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(02), pages 1-12, June.

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    More about this item

    Keywords

    Coalition formation; games in partition function form; solution concept; Cournot oligopoly.; Formation de coalition; jeu en forme de fonction de partition; concept de solution; oligopolie de Cournot.;
    All these keywords.

    JEL classification:

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

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