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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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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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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; Programming Models; Mathematical and Simulation Modeling - - - 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

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  1. Dreze, J H & Greenberg, J, 1980. "Hedonic Coalitions: Optimality and Stability," Econometrica, Econometric Society, vol. 48(4), pages 987-1003, May.
  2. Jeroen Kuipers & Ulrich Faigle & Walter Kern, 1998. "Note Computing the nucleolus of min-cost spanning tree games is NP-hard," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(3), pages 443-450.
  3. Ballester, Coralio, 2004. "NP-completeness in hedonic games," Games and Economic Behavior, Elsevier, vol. 49(1), pages 1-30, October.
  4. Tayfun Sönmez & Suryapratim Banerjee & Hideo Konishi, 2001. "Core in a simple coalition formation game," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(1), pages 135-153.
  5. Koller, Daphne & Megiddo, Nimrod, 1992. "The complexity of two-person zero-sum games in extensive form," Games and Economic Behavior, Elsevier, vol. 4(4), pages 528-552, October.
  6. Richard Baron & Jacques Durieu & Hans Haller & Rahul Savani & Philippe Solal, 2008. "Good neighbors are hard to find: computational complexity of network formation," Review of Economic Design, Springer;Society for Economic Design, vol. 12(1), pages 1-19, April.
  7. Itzhak Gilboa, 1988. "The Complexity of Computing Best-Response Automata in Repeated Games," Post-Print hal-00756286, HAL.
  8. Gilboa, Itzhak & Zemel, Eitan, 1989. "Nash and correlated equilibria: Some complexity considerations," Games and Economic Behavior, Elsevier, vol. 1(1), pages 80-93, March.
  9. Shao Sung & Dinko Dimitrov, 2007. "On Myopic Stability Concepts for Hedonic Games," Theory and Decision, Springer, vol. 62(1), pages 31-45, February.
  10. Dimitrov, D.A. & Borm, P.E.M. & Hendrickx, R.L.P. & Sung, S.C., 2006. "Simple priorities and core stability in hedonic games," Other publications TiSEM 7c737a30-ac86-46ed-b210-e, Tilburg University, School of Economics and Management.
  11. Sung, Shao Chin & Dimitrov, Dinko, 2011. "On core membership testing for hedonic coalition formation games," Center for Mathematical Economics Working Papers 374, Center for Mathematical Economics, Bielefeld University.
  12. 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.
  13. Dinko Dimitrov & Shao-Chin Sung, 2008. "Computational Complexity in Additive Hedonic Games," Working Papers 2008.98, Fondazione Eni Enrico Mattei.
  14. Ben-porath, Elchanan, 1990. "The complexity of computing a best response automaton in repeated games with mixed strategies," Games and Economic Behavior, Elsevier, vol. 2(1), pages 1-12, March.
  15. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
  16. Richard Baron & Jacques Durieu & Hans Haller & Philippe Solal & Savani Rahul, 2008. "Good neighbors are hard to find: computational complexity of network formation," Post-Print hal-00268851, HAL.
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Cited by:

  1. Sung, Shao-Chin & Dimitrov, Dinko, 2010. "Computational complexity in additive hedonic games," European Journal of Operational Research, Elsevier, vol. 203(3), pages 635-639, June.
  2. 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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