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Computational complexity in additive hedonic games

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  • Sung, Shao-Chin
  • Dimitrov, Dinko

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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Bibliographic Info

Article provided by Elsevier in its journal European Journal of Operational Research.

Volume (Year): 203 (2010)
Issue (Month): 3 (June)
Pages: 635-639

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Handle: RePEc:eee:ejores:v:203:y:2010:i:3:p:635-639

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Web page: http://www.elsevier.com/locate/eor

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Keywords: Additive preferences Coalition formation computational complexity Hedonic games NP-hard NP-complete;

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References

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  1. 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. Gilboa, Itzhak & Zemel, Eitan, 1989. "Nash and correlated equilibria: Some complexity considerations," Games and Economic Behavior, Elsevier, vol. 1(1), pages 80-93, March.
  3. Shao Chin Sung & Dinko Dimitrov, 2005. "On core membership testing for hedonic coalition formation games," Working Papers 374, Bielefeld University, Center for Mathematical Economics.
  4. 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.
  5. 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.
  6. 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.
  7. Ballester, Coralio, 2004. "NP-completeness in hedonic games," Games and Economic Behavior, Elsevier, vol. 49(1), pages 1-30, October.
  8. 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. Woeginger, Gerhard J., 2013. "A hardness result for core stability in additive hedonic games," Mathematical Social Sciences, Elsevier, vol. 65(2), pages 101-104.

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