We study coalitional games where the coalitional payoffs depend on the embedding coalition structure. We introduce a noncooperative, sequential coalition formation model and show that the set of equilibrium outcomes coincides with the recursive core, a generalisation of the core to such games. In order to extend past results limited to totally recursive-balanced partition function form games we introduce a more permissive perfectness concept, subgame-consistency that only requires perfectness

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... selected subgames. Due to the externalities, the profitability of deviations depends on the partition formed by the remaining players: the stability of core payoff configurations is ensured by a combination of the pessimism of players going for certain profits only and the assumption that players base their stationary strategies * The author thanks Lars Ehlers for his comments and the Hungarian Academy of Sciences for the financial support (LP-004/2010).