Revising claims and resisting ultimatums in bargaining problems

We propose a mechanism which implements a unique solution to the bargaining problem with two players in subgame-perfect equilibrium. Players start by making claims and accept a compromise only if they cannot gain by pursuing their claim in an ultimatum. The player offering the lowest resistance to his opponent’s claim can propose a compromise. The unique solution depends on the extent to which claims can be revised. If no revisions are allowed, compatible claims implement the Nash solution. If all revisions are allowed, maximal claims implement the Kalai-Smorodinsky solution.