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A note on the paradox of smaller coalitions

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  • Dinko Dimitrov

    ()
    (Institute of Mathematical Economics, Bielefeld University)

  • Claus-Jochen Haake

    ()
    (Institute of Mathematical Economics, Bielefeld University)

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 winning coalition containing that player, then the induced hedonic game satisfies the top coalition property.

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File URL: http://www.imw.uni-bielefeld.de/papers/files/imw-wp-386.pdf
File Function: First version, 2006
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Bibliographic Info

Paper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 386.

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Length: 11 pages
Date of creation: Dec 2006
Date of revision:
Handle: RePEc:bie:wpaper:386

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Related research

Keywords: coalition formation; core; paradox of smaller coalitions; simple games; top coalition property;

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References

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  1. 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.
  2. Tayfun Sönmez & Suryapratim Banerjee & Hideo Konishi, 2001. "Core in a simple coalition formation game," Social Choice and Welfare, Springer, vol. 18(1), pages 135-153.
  3. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
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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, 2013. "Bargaining and Power," Working Papers 2013.63, Fondazione Eni Enrico Mattei.

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