ar X iv : 1 10 5 . 18 24 v 2 [ cs . G T ] 3 D ec 2 01 1 Individual - based stability in hedonic games depending on the best or worst players ∗

We consider hedonic coalition formation games in which each player has preferences over the other players and his preferences over coalition structures are based on the best player (B-/B-hedonic games) or the worst player (W /W-hedonic games) in his coalition. We show that for B-hedonic games, an individually stable partition is guaranteed to exist and can be computed efficiently. Similarly, there exists a polynomial-time algorithm which returns a Nash stable partition (if one exists) for B-hedonic games with strict preferences. It is also shown that for Band W -hedonic games, checking whether a Nash stable partition or an individually stable partition exists is NP-complete even in some cases for strict preferences. As a result of our investigation, we identify a key source of intractability in compact coalition formation games in which preferences over players are extended to preferences over coalitions.