We study strategic three-player coalitional bargaining problems in an environment with externalities where contracts forming coalitions can be written and renegotiated. The theory yields a unique stationary subgame perfect Nash equilibrium outcome (the coalitional bargaining value). This solution has an intuitive economic interpretation using outside options, and it can be either the Nash bargaining solution, for games where the worth of all pairwise coalition is less than a third of the grand coalition value; the Shapely value, for games where the sum of the values created by all pairwise coalitions is greater than the grand coalition value; or the nucleolus, for games where only the 'natural coalition' among two 'natural partners' creates significant value, and those where only the pairwise coalitions including 'a pivotal player' create significant value.