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A coalition formation value for games with externalities

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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 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, 2008. "A coalition formation value for games with externalities," Documents de travail du Centre d'Economie de la Sorbonne b08076, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:b08076
    DOI: 10.1016/j.ejor.2012.02.036
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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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    JEL classification:

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

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