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Abstract

A pure hedonic game describes the situation where player's utility depends only on the identity of the members of the group he belongs to. The paper provides a necessary and sufficient condition for the existence of core-partition in hedonic games. The condition is based on a new concept of balancedness, called pivotal balancedness. pivotal balancedness involves especially the notion pivotal distribution that associates to each coalition a sub-group of players in the coalition. Then, we proceed to a review of several sufficient conditions for core-partition existence showing how the results can be unified through suitably chosen pivotal distributions.

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File URL: ftp://mse.univ-paris1.fr/pub/mse/cahiers2005/B05091.pdf
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Bibliographic Info

Paper provided by Université Panthéon-Sorbonne (Paris 1) in its series Cahiers de la Maison des Sciences Economiques with number b05091.

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Length: 11 pages
Date of creation: Dec 2005
Date of revision:
Handle: RePEc:mse:wpsorb:b05091

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Related research

Keywords: Hedonic game; group formation; core-partition; balancedness.;

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Find related papers by JEL classification:

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

This paper has been announced in the following NEP Reports:

• NEP-ALL-2006-01-24 (All new papers)
• NEP-GTH-2006-01-24 (Game Theory)

References

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1. Dinko Dimitrov & Peter Borm, 2004. "Simple Priorities and Core Stability in Hedonic Games," Econometric Society 2004 North American Summer Meetings 135, Econometric Society.
   
   • Dinko Dimitrov & Peter Borm & Ruud Hendrickx & Shao Sung, 2006. "Simple Priorities and Core Stability in Hedonic Games," Social Choice and Welfare, Springer, vol. 26(2), pages 421-433, April.
   • Dinko Dimitrov & Peter Borm & Ruud Hendrickx & Shao Chin Sung, 2004. "Simple Priorities and Core Stability in Hedonic Games," Working Papers 2004.51, Fondazione Eni Enrico Mattei.
   • Dimitrov, D.A. & Borm, P.E.M. & Hendrickx, R.L.P. & Sung, S.C., 2006. "Simple priorities and core stability in hedonic games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-194178, Tilburg University.
   • Dimitrov, D.A. & Borm, P.E.M. & Hendrickx, R.L.P. & Sung, S.C., 2004. "Simple Priorities and Core Stability in Hedonic Games," Discussion Paper 2004-5, Tilburg University, Center for Economic Research.
2. Herbert E. Scarf, 1965. "The Core of an N Person Game," Cowles Foundation Discussion Papers 182R, Cowles Foundation for Research in Economics, Yale University.
3. Predtetchinski, Arkadi & Jean-Jacques Herings, P., 2004. "A necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game," Journal of Economic Theory, Elsevier, vol. 116(1), pages 84-92, May.
   
   • Predtetchinski, Arkadi & Herings, P. Jean-Jacques, 2004. "A necessary and sufficient condition for nonemptiness of the core of a non-transferable utility game," Open Access publications from Maastricht University urn:nbn:nl:ui:27-12168, Maastricht University.
   • Herings,P. Jean-Jacques & Predtetchinski,Arkadi, 2002. "A Necessary and Sufficient Condition for Non--emptiness of the Core of a Non--transferable Utility Game," Research Memoranda 016, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization.
4. Szilvia Papai, 2000. "Unique Stability in Simple Coalition Formation Games," Econometric Society World Congress 2000 Contributed Papers 1537, Econometric Society.
   
   • Papai, Szilvia, 2004. "Unique stability in simple coalition formation games," Games and Economic Behavior, Elsevier, vol. 48(2), pages 337-354, August.
5. BOGOMOLNAIA, Anna & LE BRETON, Michel & SAVVATEEV, Alexei & WEBER, Shlomo, 2005. "Stability of jurisdiction structures under the equal share and median rules," CORE Discussion Papers 2005032, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
   
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   • Bogomolnaia, Anna & Le Breton, Michel & Savvateev, Alexei & Weber, Shlomo, 2008. "Stability of Jurisdiction Structures under the Equal Share and Median Rule," Open Access publications from University of Toulouse 1 Capitole http://neeo.univ-tlse1.fr, University of Toulouse 1 Capitole.
   • Bogomolnaia, Anna & Le Breton, Michel & Savvateev, Alexei & Weber, Shlomo, 2005. "Stability of Jurisdiction Structures under the Equal Share and Median Rule," IDEI Working Papers 362, Institut d'Économie Industrielle (IDEI), Toulouse.
6. Greenberg, Joseph & Weber, Shlomo, 1986. "Strong tiebout equilibrium under restricted preferences domain," Journal of Economic Theory, Elsevier, vol. 38(1), pages 101-117, February.
7. Burani, Nadia & Zwicker, William S., 2003. "Coalition formation games with separable preferences," Mathematical Social Sciences, Elsevier, vol. 45(1), pages 27-52, February.
8. Bonnisseau, Jean-Marc & Iehle, Vincent, 2007. "Payoff-dependent balancedness and cores," Games and Economic Behavior, Elsevier, vol. 61(1), pages 1-26, October.
   
   • Bonnisseau, Jean-Marc & Iehlé, Vincent, 2007. "Payoff-dependant Balancedness and Cores," Open Access publications from Université Paris-Dauphine urn:hdl:123456789/89, Université Paris-Dauphine.
   • Jean-Marc Bonnisseau & Vincent Iehle, 2004. "Payoffs-dependent Balancedness and Cores," Game Theory and Information 0403004, EconWPA.
9. 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.
   
   • 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.
10. Mamoru Kaneko & Myrna Holtz Wooders, 1982. "Cores of Partitioning Games," Cowles Foundation Discussion Papers 620, Cowles Foundation for Research in Economics, Yale University.
    
    • Kaneko, Mamoru & Wooders, Myrna Holtz, 1982. "Cores of partitioning games," Mathematical Social Sciences, Elsevier, vol. 3(4), pages 313-327, December.
11. Dreze, J H & Greenberg, J, 1980. "Hedonic Coalitions: Optimality and Stability," Econometrica, Econometric Society, vol. 48(4), pages 987-1003, May.
    
    • Dreze, Jacques, 1980. "Hedonic coalitions : optimality and stability," Open Access publications from Université catholique de Louvain info:hdl:2078.1/88260, Université catholique de Louvain.

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Citations

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Cited by:

1. Alparslan Gök, S.Z. & Branzei, O. & Branzei, R. & Tijs, S., 2011. "Set-valued solution concepts using interval-type payoffs for interval games," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 621-626.
2. Karakaya, Mehmet, 2011. "Hedonic coalition formation games: A new stability notion," Mathematical Social Sciences, Elsevier, vol. 61(3), pages 157-165, May.
3. Hans Gersbach & Hans Haller, 2011. "Bargaining cum voice," Social Choice and Welfare, Springer, vol. 36(2), pages 199-225, February.
   
   • Gersbach, Hans & Haller, Hans, 2010. "Bargaining cum Voice," CEPR Discussion Papers 7774, C.E.P.R. Discussion Papers.
4. Fan-Chin Kung, 2010. "Coalition formation with local public goods and group-size effect," International Journal of Game Theory, Springer, vol. 39(4), pages 573-583, October.

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