Computational Complexity in Additive Hedonic Games

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Computational Complexity in Additive Hedonic Games

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Sung, Shao-Chin
Dimitrov, Dinko

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Dinko Dimitrov

Abstract

We investigate the computational complexity of several decision problems in hedonic coalition formation games and demonstrate that attaining stability in such games remains NP-hard even when they are additive. Precisely, we prove that when either core stability or strict core stability is under consideration, the existence problem of a stable coalition structure is NP-hard in the strong sense. Furthermore, the corresponding decision problems with respect to the existence of a Nash stable coalition structure and of an individually stable coalition structure turn out to be NP-complete in the strong sense.

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Paper provided by University of Munich, Department of Economics in its series Discussion Papers in Economics with number 6430.

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Date of creation: 07 Oct 2008
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Handle: RePEc:lmu:muenec:6430

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Paper
- Dinko Dimitrov & Shao-Chin Sung, 2008. "Computational Complexity in Additive Hedonic Games," Working Papers 2008.98, Fondazione Eni Enrico Mattei. [Downloadable!]

Find related papers by JEL classification:
C63 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Computational Techniques
C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

This paper has been announced in the following NEP Reports:

NEP-ALL-2008-10-21 (All new papers)
NEP-GTH-2008-10-21 (Game Theory)

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

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. [Downloadable!] (restricted)
Other versions:
- 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. [Downloadable!]
Shao Chin Sung & Dinko Dimitrov, 2005. "On core membership testing for hedonic coalition formation games," Working Papers 374, Bielefeld University, Institute of Mathematical Economics. [Downloadable!]
Gilboa, Itzhak & Zemel, Eitan, 1989. "Nash and correlated equilibria: Some complexity considerations," Games and Economic Behavior, Elsevier, vol. 1(1), pages 80-93, March. [Downloadable!] (restricted)
Other versions:
- Itzhak Gilboa & Eitan Zemel, 1988. "Nash and Correlated Equilibria: Some Complexity Considerations," Discussion Papers 777, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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. [Downloadable!] (restricted)
Other versions:
- 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. [Downloadable!]
- Dinko Dimitrov & Peter Borm, 2004. "Simple Priorities and Core Stability in Hedonic Games," Econometric Society 2004 North American Summer Meetings 135, Econometric Society. [Downloadable!]
- Dimitrov, D. & Borm, P.E.M. & Hendrickx, R.L.P. & Sung, S.C., 2004. "Simple priorities and core stability in hedonic games," Discussion Paper 5, Tilburg University, Center for Economic Research. [Downloadable!]
Gilboa, Itzhak, 1988. "The complexity of computing best-response automata in repeated games," Journal of Economic Theory, Elsevier, vol. 45(2), pages 342-352, August. [Downloadable!] (restricted)
Ballester, Coralio, 2004. "NP-completeness in hedonic games," Games and Economic Behavior, Elsevier, vol. 49(1), pages 1-30, October. [Downloadable!] (restricted)
Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February. [Downloadable!] (restricted)
Koller, Daphne & Megiddo, Nimrod & von Stengel, Bernhard, 1996. "Efficient Computation of Equilibria for Extensive Two-Person Games," Games and Economic Behavior, Elsevier, vol. 14(2), pages 247-259, June. [Downloadable!] (restricted)

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