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A coalition formation value for games in partition function form

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  • Michel Grabisch

    () (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Yukihiko Funaki

    (School of political science and economics, Waseda University - Waseda university)

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 also two axiomatizations of our coalition formation value.

Suggested Citation

  • Michel Grabisch & Yukihiko Funaki, 2012. "A coalition formation value for games in partition function form," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00690696, HAL.
  • Handle: RePEc:hal:cesptp:halshs-00690696 Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00690696
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    References listed on IDEAS

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    1. Ray, Debraj & Vohra, Rajiv, 1997. "Equilibrium Binding Agreements," Journal of Economic Theory, Elsevier, vol. 73(1), pages 30-78, March.
    2. Diamantoudi, Effrosyni & Xue, Licun, 2007. "Coalitions, agreements and efficiency," Journal of Economic Theory, Elsevier, vol. 136(1), pages 105-125, September.
    3. Gilboa, Itzhak & Lehrer, Ehud, 1991. "Global Games," International Journal of Game Theory, Springer;Game Theory Society, pages 129-147.
    4. Michel Grabisch, 2010. "The lattice of embedded subsets," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00457827, HAL.
    5. Geoffroy de Clippel & Roberto Serrano, 2008. "Marginal Contributions and Externalities in the Value," Econometrica, Econometric Society, vol. 76(6), pages 1413-1436, November.
    6. 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.
    7. 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.
    8. Macho-Stadler, Ines & Perez-Castrillo, David & Wettstein, David, 2007. "Sharing the surplus: An extension of the Shapley value for environments with externalities," Journal of Economic Theory, Elsevier, vol. 135(1), pages 339-356, July.
    9. Yukihiko Funaki & Takehiko Yamato, 1999. "The core of an economy with a common pool resource: A partition function form approach," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(2), pages 157-171.
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    Cited by:

    1. In?s Macho-Stadler & David P?rez-Castrillo & David Wettstein, 2017. "Extensions Of The Shapley Value For Environments With Externalities," Working Papers 1716, Ben-Gurion University of the Negev, Department of Economics.
    2. Ulrich Faigle & Michel Grabisch, 2012. "Values for Markovian coalition processes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 505-538.
    3. Dávid Csercsik & Balázs Sziklai, 2015. "Traffic routing oligopoly," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 23(4), pages 743-762, December.
    4. Nessah, Rabia & Tazdaı¨t, Tarik, 2013. "Absolute optimal solution for a compact and convex game," European Journal of Operational Research, Elsevier, vol. 224(2), pages 353-361.
    5. van den Brink, René & González-Arangüena, Enrique & Manuel, Conrado & del Pozo, Mónica, 2014. "Order monotonic solutions for generalized characteristic functions," European Journal of Operational Research, Elsevier, vol. 238(3), pages 786-796.
    6. Vincent Iehlé, 2015. "The lattice structure of the S-Lorenz core," Theory and Decision, Springer, pages 141-151.
    7. Bloch, Francis & van den Nouweland, Anne, 2014. "Expectation formation rules and the core of partition function games," Games and Economic Behavior, Elsevier, vol. 88(C), pages 339-353.
    8. repec:wsi:igtrxx:v:19:y:2017:i:02:n:s0219198917500074 is not listed on IDEAS

    More about this item

    Keywords

    game theory; coalition formation; games in partition function form; Shapley value;

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