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Autonomous coalitions

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Abstract

We consider in this paper solutions for TU-games where it is not assumed that the grand coalition is necessarily the final state of cooperation. Partitions of the grand coalition, or balanced collections together with a system of balancing weights interpreted as a time allocation vector are considered as possible states of cooperation. The former case corresponds to the c-core, while the latter corresponds to the aspiration core or d-core, where in both case, the best configuration (called a maximising collection) is sought. We study maximising collections and characterize them with autonomous coalitions, that is, coalitions for which any solution of the d-core yields a payment for that coalition equal to its worht. In particular we show that the collection of autonomous coalitions is balanced, and that one cannot have at the same time a single possible payment (core element) and a single possible configuration. We also introduce the notion of inescapable coalitions, that is, those present in every maximising collection. We characterize the class of games for which the sets of autonomous coalitions, vital coalitions (in the sense of Shellshear and Sudhölter), and inescapable coalitions coincide, and prove that the set of games having a unique maximising coalition is dense in the set of games

Suggested Citation

  • Stéphane Gonzalez & Michel Grabisch, 2014. "Autonomous coalitions," Documents de travail du Centre d'Economie de la Sorbonne 14044, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  • Handle: RePEc:mse:cesdoc:14044
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    File URL: ftp://mse.univ-paris1.fr/pub/mse/CES2014/14044.pdf
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    References listed on IDEAS

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    1. Sun, Ning & Trockel, Walter & Yang, Zaifu, 2008. "Competitive outcomes and endogenous coalition formation in an n-person game," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 853-860, July.
    2. Camelia Bejan & Juan Gómez, 2012. "Axiomatizing core extensions," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 885-898, November.
    3. Stéphane Gonzalez & Michel Grabisch, 2015. "Preserving coalitional rationality for non-balanced games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(3), pages 733-760, August.
    4. repec:wsi:igtrxx:v:14:y:2012:i:01:n:s0219198912500041 is not listed on IDEAS
    5. repec:hal:journl:hal-00321625 is not listed on IDEAS
    6. Michel Grabisch & Pedro Miranda, 2008. "On the vertices of the k-additive core," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00321625, HAL.
    7. Derks, Jean & Peters, Hans, 1998. "Orderings, excess functions, and the nucleolus," Mathematical Social Sciences, Elsevier, vol. 36(2), pages 175-182, September.
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    Cited by:

    1. Stéphane Gonzalez & Aymeric Lardon, 2016. "Optimal Deterrence of Cooperation," Working Papers 1621, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.

    More about this item

    Keywords

    Cooperative game; core; balancedness; c-core; aspiration core; coalition formation; autonomous coalitions;

    JEL classification:

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

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