Nash Stability in Additively Separable Hedonic Games Is NP-Hard
Ballester has shown that the problem of deciding whether a Nash stable partition exists in a hedonic game with arbitrary preferences is NP-complete. In this paper we will prove that the problem remains NP-complete even when restricting to additively separable hedonic games.
Bogomolnaia and Jackson have shown that a Nash stable partition exists in every additively separable hedonic game with symmetric preferences. We show that computing Nash stable partitions is hard in games with symmetric preferences. To be more specific we 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. The corresponding problem concerning individual stability is also NP-complete since individually stable partitions are Nash stable and vice versa in such games.
KeywordsNash Stability Hedonic Games NP-Completeness
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