The core is reformulated to incorporate the externality typical in strategic form games. Any coalition of players may deviate by trying to commit to a profile of actions different from a status quo. The outsiders of the coalition may take a coordinated measure, incentive-feasibly for themselves, to preempt the coalition's commitment. If a coalition succeeds in committing to its action profile, the outsiders' reactions constitute a core solution among themselves. A core solution is robust against the deviations of coalitions which expect such preemptive and reactive responses from the other players. In an externality problem where pollution is the dominant action, the core is nonempty. In any two-player strategic form game, the core is also nonempty.