Pareto Optimality in Coalition Formation

  • Haris Aziz
  • Felix Brandt
  • Paul Harrenstein
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6982)


A minimal requirement on allocative efficiency in the social sciences is Pareto optimality. In this paper, we identify a far-reaching structural connection between Pareto optimal and perfect partitions that has various algorithmic consequences for coalition formation. In particular, we show that computing and verifying Pareto optimal partitions in general hedonic games and B-hedonic games is intractable while both problems are tractable for roommate games and W-hedonic games. The latter two positive results are obtained by reductions to maximum weight matching and clique packing, respectively.


Polynomial Time Coalition Formation Pareto Optimality Coalition Structure Grand Coalition 
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  1. 1.
    Abdulkadiroğlu, A., Sönmez, T.: Random serial dictatorship and the core from random endowments in house allocation problems. Econometrica 66(3), 689–702 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Ballester, C.: NP-completeness in hedonic games. Games and Economic Behavior 49(1), 1–30 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Banerjee, S., Konishi, H., Sönmez, T.: Core in a simple coalition formation game. Social Choice and Welfare 18, 135–153 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Bogomolnaia, A., Jackson, M.O.: The stability of hedonic coalition structures. Games and Economic Behavior 38(2), 201–230 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Cechlárová, K.: On the complexity of exchange-stable roommates. Discrete Applied Mathematics 116, 279–287 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Cechlárová, K., Hajduková, J.: Stable partitions with \(\mathcal{W}\)-preferences. Discrete Applied Mathematics 138(3), 333–347 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Cechlárová, K., Hajduková, J.: Stability of partitions under \(\mathcal{BW}\)-preferences and \(\mathcal{WB}\)-preferences. International Journal of Information Technology and Decision Making 3(4), 605–618 (2004)CrossRefGoogle Scholar
  8. 8.
    Cornuéjols, G., Hartvigsen, D., Pulleyblank, W.: Packing subgraphs in a graph. Operations Research Letters 1(4), 139–143 (1982)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Drèze, J.H., Greenberg, J.: Hedonic coalitions: Optimality and stability. Econometrica 48(4), 987–1003 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Hell, P., Kirkpatrick, D.G.: Packings by cliques and by finite families of graphs. Discrete Mathematics 49(1), 45–59 (1984)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Morrill, T.: The roommates problem revisited. Journal of Economic Theory 145(5), 1739–1756 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Ronn, E.: NP-complete stable matching problems. Journal of Algorithms 11, 285–304 (1990)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Haris Aziz
    • 1
  • Felix Brandt
    • 1
  • Paul Harrenstein
    • 1
  1. 1.Institut für InformatikTechnische Universität MünchenMünchenGermany

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