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Computational Complexity in Additive Hedonic Games

  • Sung, Shao-Chin
  • Dimitrov, Dinko

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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File URL: http://epub.ub.uni-muenchen.de/6430/1/Complexity.pdf
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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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  1. Dinko Dimitrov & Peter Borm, 2004. "Simple Priorities and Core Stability in Hedonic Games," Econometric Society 2004 North American Summer Meetings 135, Econometric Society.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. Shao Chin Sung & Dinko Dimitrov, 2005. "On core membership testing for hedonic coalition formation games," Center for Mathematical Economics Working Papers 374, Center for Mathematical Economics, Bielefeld University.
  7. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
  8. Ballester, Coralio, 2004. "NP-completeness in hedonic games," Games and Economic Behavior, Elsevier, vol. 49(1), pages 1-30, October.
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