Social Choice and Welfare

, Volume 30, Issue 4, pp 571–579 | Cite as

A note on the paradox of smaller coalitions

  • Dinko Dimitrov
  • Claus-Jochen Haake
Original Paper


We consider hedonic coalition formation games that are induced by a simple TU-game and a cooperative solution. For such models, Shenoy’s (Int J Game Theory 8:133–164, 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. (Social Choice Welfare 18:135–153, 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.


Coalition Structure Simple Game Winning Coalition Core Stability Minimal Winning Coalition 
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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Chair of Microeconomic Theory, Faculty of Law and EconomicsUniversity of BayreuthBayreuthGermany
  2. 2.Institute of Mathematical EconomicsBielefeld UniversityBielefeldGermany

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