Abstract 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 in 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 on a made-up
history punishing some of the possible deviators—and getting this sometimes right.
