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Stable Coalition Structures: Characterizations and Applications of Hart and Kurz's Four Stability Concepts

Author

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  • Takaaki Abe

    (Graduate School of Economics, Waseda University)

Abstract

Hart and Kurz (1983) introduced four stability concepts, called α-, β-, γ-, and δ-stability. In contrast to the intensive studies on their conceptual aspects, these notions have rarely been adopted to analyze stable coalition structures in an application because the definitions consist of multiple intermediate steps. The purpose of this paper is to solve these practical difficulties. We provide an explicit form for each of the four stability concepts and reformulate each concept without using any intermediate steps. Moreover, we offer some sufficient conditions that guarantee the existence of stable coalition structures and the inclusion relation among the four stability notions. In addition, we propose a new approach to characterize the notions of stability. An application of our results to Cournot oligopoly is also provided.

Suggested Citation

  • Takaaki Abe, 2019. "Stable Coalition Structures: Characterizations and Applications of Hart and Kurz's Four Stability Concepts," Working Papers 1812, Waseda University, Faculty of Political Science and Economics.
    • Handle: RePEc:wap:wpaper:1812
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    References listed on IDEAS

    as
    1. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-1064, July.
    2. Harald Wiese, 2007. "Measuring The Power Of Parties Within Government Coalitions," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 9(02), pages 307-322.
    3. Ray, Debraj & Vohra, Rajiv, 1997. "Equilibrium Binding Agreements," Journal of Economic Theory, Elsevier, vol. 73(1), pages 30-78, March.
    4. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
    5. Yi, Sang-Seung, 1997. "Stable Coalition Structures with Externalities," Games and Economic Behavior, Elsevier, vol. 20(2), pages 201-237, August.
    6. Takaaki Abe, 2018. "Stable coalition structures in symmetric majority games: a coincidence between myopia and farsightedness," Theory and Decision, Springer, vol. 85(3), pages 353-374, October.
    7. Yoshio Kamijo, 2009. "A Two-Step Shapley Value For Cooperative Games With Coalition Structures," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 11(02), pages 207-214.
    8. AUMANN, Robert J. & DREZE, Jacques H., 1974. "Cooperative games with coalition structures," LIDAM Reprints CORE 217, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    Full references (including those not matched with items on IDEAS)

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    JEL classification:

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

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