Individual-based stability in hedonic games depending on the best or worst players

We consider classes of hedonic games in which each player’s preferences over coalition structures are induced by the best player (Band B-hedonic games) or the worst player (Wand W-hedonic games) in his coalition. For these classes, which allow for concise representation, we analyze the computational complexity of deciding the existence of and computing individually stable, Nash stable, and individually rational and contractually individually stable coalition partitions. We identify a key source of intractability in compact coalition formation games in which preferences over players are extended to preferences over coalitions.