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We consider coalition formation games in which each player has preferencesover the other players and his preferences over coalitions are based on thebest 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 toexist and can be computed efficiently. Similarly, there exists apolynomial-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 isalso shown that for B- or $\mathcal{W}$-hedonic games, checking whether a Nashstable partition or an individually stable partition exists is NP-complete evenin some cases for strict preferences. We identify a key source ofintractability in compact coalition formation games in which preferences overplayers are extended to preferences over coalitions.

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