models, Shenoy's (1979) absence of the paradox of smaller coalitions provides a sufficient condition for core existence. We …. (2001) that guarantees nonemptiness of the core in more general models. As it turns out, the top coalition property implies … induced hedonic game satisfies the top coalition property. -- Coalition formation ; Core ; Paradox of smaller coalitions …

the clan by a "dualize and extend" procedure. These procedures are also useful for relating core elements and elements of … the Weber set of the corresponding games. -- Convex games ; Core , Dual games ; Marginal games ; Total clan games ; Weber …

We are concerned with the problem of core membership testing for hedonic coalition formation games, which is to decide … whether a certain coalition structure belongs to the core of a given game. We show that this problem is co-NP complete when … players' preferences are additive. -- Additivity ; Coalition formation ; Core ; Co-NP completeness ; Hedonic games …