A note on the paradox of smaller coalitions
AbstractWe 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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Bibliographic InfoPaper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 386.
Length: 11 pages
Date of creation: Dec 2006
Date of revision:
coalition formation; core; paradox of smaller coalitions; simple games; top coalition property;
Other versions of this item:
- D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
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- Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
- Suryapratim Banerjee & Hideo Konishi & Tayfun Sonmez, 1999.
"Core in a Simple Coalition Formation Game,"
Boston College Working Papers in Economics
449, Boston College Department of Economics.
- Dinko Dimitrov & Claus-Jochen Haake, 2005.
"Government versus opposition: Who should be who in the 16th German Bundestag?,"
375, Bielefeld University, Center for Mathematical Economics.
- 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.
- Dominik Karos, 2013. "Coalition Formation in General Apex Games," Economics Series Working Papers 680, University of Oxford, Department of Economics.
- Dominik Karos, 2013. "Bargaining and Power," Working Papers 2013.63, Fondazione Eni Enrico Mattei.
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