Skip to main content
SpringerLink
Log in

Nash Stability in Additively Separable Hedonic Games and Community Structures

  • Published:
Theory of Computing Systems Aims and scope Submit manuscript

Abstract

We prove that the problem of deciding whether a Nash stable partition exists in an Additively Separable Hedonic Game is NP-complete. We also show that the problem of deciding whether a non trivial Nash stable partition exists in an Additively Separable Hedonic Game with non-negative and symmetric preferences is NP-complete. We motivate our study of the computational complexity by linking Nash stable partitions in Additively Separable Hedonic Games to community structures in networks. Our results formally justify that computing community structures in general is hard.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ballester, C.: NP-completeness in hedonic games. Games Econ. Behav. 49(1), 1–30 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  2. Burani, N., Zwicker, W.S.: Coalition formation games with separable preferences. Math. Soc. Sci. 45(1), 27–52 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  3. Cechlárová, K., Hajduková, J.: Computational complexity of stable partitions with b-preferences. Int. J. Game Theory 31(3), 353–364 (2002)

    MATH  Google Scholar 

  4. Cechlárová, K., Hajduková, J.: Stable partitions with w-preferences. Discrete Appl. Math. 138(3), 333–347 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  5. Chen, N., Rudra, A.: Walrasian equilibrium: Hardness, approximations and tractable instances. In: WINE, pp. 141–150 (2005)

  6. Daskalakis, K., Papadimitriou, C.H.: The complexity of games on highly regular graphs. In: ESA, pp. 71–82 (2005)

  7. Duch, J., Danon, L., Díaz-Guilera, A., Arenas, A.: Comparing community structure identification. J. Stat. Mech. Theory Exp. 2005(09), 09008 (2005)

    Article  Google Scholar 

  8. Flake, G., Tarjan, R., Tsioutsiouliklis, K.: Graph clustering and minimum cut trees. Internet Math. 1(4), 385–408 (2004)

    MATH  MathSciNet  Google Scholar 

  9. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, New York (1979)

    MATH  Google Scholar 

  10. Hajdukova, J.: On coalition formation games. Technical Report, Institute of Mathematics, PJ Safarik University (2004)

  11. Jackson, M.O., Bogomolnaia, A.: The stability of hedonic coalition structures. Games Econ. Behav. 38(2), 201–230 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  12. Newman, M.E.J., Girvan, M.: Finding and evaluating community structure in networks. Phys. Rev. E 69, 026113 (2004)

    Article  Google Scholar 

  13. Sung, S.C., Dimitrov, D.: On core membership testing for hedonic coalition formation games. Oper. Res. Lett. 35(2), 155–158 (2007)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. MADALGO, Department of Computer Science, University of Aarhus, Aabogade 34, 8200, Aarhus N, Denmark

    Martin Olsen

Authors
  1. Martin Olsen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Martin Olsen.

Additional information

The research is partly sponsored by the company Cofman (www.cofman.com).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Olsen, M. Nash Stability in Additively Separable Hedonic Games and Community Structures. Theory Comput Syst 45, 917–925 (2009). https://doi.org/10.1007/s00224-009-9176-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00224-009-9176-8

Keywords

Search

Navigation