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A note on the paradox of smaller coalitions

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  • Dinko Dimitrov
  • Claus-Jochen Haake

Abstract

We consider hedonic coalition formation games that are induced by a simple TU-game and a cooperative solution. For such models, Shenoy's (1979) absence of the paradox of smaller coalitions provides a sufficient condition for core existence. We present three different versions of his condition in order to compare it to the top coalition property of Banerjee et al. (2001) that guarantees nonemptiness of the core in more general models. As it turns out, the top coalition property implies a condition in which Shenoy's paradox is not present for at least one minimal winning coalition. Conversely, if for each non-null player Shenoy's paradox is not present for at least one minimal winnig coalition containing that player, then the induced hedonic game satisfies the top coalition property.
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  • Dinko Dimitrov & Claus-Jochen Haake, 2008. "A note on the paradox of smaller coalitions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(4), pages 571-579, May.
    • Handle: RePEc:spr:sochwe:v:30:y:2008:i:4:p:571-579
    DOI: 10.1007/s00355-007-0266-8
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    References listed on IDEAS

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    1. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
    2. Tayfun Sönmez & Suryapratim Banerjee & Hideo Konishi, 2001. "Core in a simple coalition formation game," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(1), pages 135-153.
    3. Dinko Dimitrov & Claus-Jochen Haake, 2006. "Government versus Opposition: Who Should be Who in the 16th German Bundestag?," Journal of Economics, Springer, vol. 89(2), pages 115-128, November.
    4. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
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    Cited by:

    1. Dominik Karos, 2013. "Coalition Formation in General Apex Games," Economics Series Working Papers 680, University of Oxford, Department of Economics.
    2. Dominik Karos, 2015. "Stable partitions for games with non-transferable utilities and externalities," Economics Series Working Papers 741, University of Oxford, Department of Economics.
    3. Dominik Karos, 2016. "A note on monotonic power indices, smaller coalitions, and new members," Theory and Decision, Springer, vol. 81(1), pages 89-100, June.
    4. Dominik Karos, 2013. "Bargaining and Power," Working Papers 2013.63, Fondazione Eni Enrico Mattei.
    5. Karos, Dominik, 2014. "Coalition formation in general apex games under monotonic power indices," Games and Economic Behavior, Elsevier, vol. 87(C), pages 239-252.

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