The paper examines bargaining over a one--dimensional set of social states, with a unanimity acceptance rule. We consider a class of delta-equilibria, i.e. subgame perfect equilibria in stationary strategies that are free of coordination failures in the response stage.We show that along any sequence of delta-equilibria, as delta converges to one, the proposal of each player converges to the same limit. The limit, called the bargaining outcome, is uniquely determined by the set of players, the recognition probabilities, and the utility functions, and it is independent of the choice of the sequence. We characterize the bargaining outcome as a unique solution of a characteristic equation.