Toward the complexity of the existence of wonderfully stable partitions and strictly core stable coalition structures in enemy-oriented hedonic games

  • Anja Rey
  • Jörg Rothe
  • Hilmar Schadrack
  • Lena SchendEmail author


We study the computational complexity of the existence and the verification problem for wonderfully stable partitions (WSPE and WSPV) and of the existence problem for strictly core stable coalition structures (SCSCS) in enemy-oriented hedonic games. In this note, we show that WSPV is NP-complete and both WSPE and SCSCS are DP-hard, where DP is the second level of the boolean hierarchy, and we discuss an approach for classifying the latter two problems in terms of their complexity.


Game Theory Hedonic games Strict core stability Wonderful stability 

Mathematics Subject Classification (2010)

68Q15 68Q17 91A12 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Anja Rey
    • 1
  • Jörg Rothe
    • 1
  • Hilmar Schadrack
    • 1
  • Lena Schend
    • 1
    Email author
  1. 1.Institut für InformatikHeinrich-Heine-Universität DüsseldorfDüsseldorfGermany

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