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Computational Complexity in Additive Hedonic Games

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Author Info
Dinko Dimitrov (University of Munich)
Shao-Chin Sung (Aoyama Gakuin University)

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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 Fondazione Eni Enrico Mattei in its series Working Papers with number 2008.98.

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Date of creation: Dec 2008
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Handle: RePEc:fem:femwpa:2008.98

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Related research
Keywords: Additive Preferences; Coalition Formation; Computational Complexity; Hedonic Games; NP-hard; NP-complete;

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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
D02 - Microeconomics - - General - - - Institutions: Design, Formation, and Operations
D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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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.:
  1. 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)
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  2. 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!]
  3. 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)
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  4. 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)
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  5. 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)
  6. Ballester, Coralio, 2004. "NP-completeness in hedonic games," Games and Economic Behavior, Elsevier, vol. 49(1), pages 1-30, October. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  8. 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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