  We consider coalition formation games in which each player has preferences
over the other players and his preferences over coalitions are based on the
best player ($\mathcal{B}$-/B-hedonic games) or the worst player
($\mathcal{W}$/W-hedonic games) in the coalition. We show that for
$\mathcal{B}$-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 $\mathcal{B}$-hedonic games with strict preferences. Both $\mathcal{W}$-
and W-hedonic games are equivalent if individual rationality is assumed. It is
also shown that for B- or $\mathcal{W}$-hedonic games, checking whether a Nash
stable partition or an individually stable partition exists is NP-complete even
in some cases for strict preferences. We identify a key source of
intractability in compact coalition formation games in which preferences over
players are extended to preferences over coalitions.
