Most real-life bargaining is resolved gradually; two parties reach intermediate agreements without knowing the whole range of possibilities. These intermediate agreements serve as disagreement points in subsequent rounds. Cooperative bargaining solutions ignore these dynamics and can therefore yield accurate predictions only if they are robust to its specification. We identify robustness criteria which are satisfied by four of the best-known bargaining solutions, the Nash, Kalai-Smorodinsky, Proportional and Discrete Raiffa solutions. We show that the “robustness of intermediate agreements” plus additional well-known and plausible axioms, provide the first characterization of the Discrete Raiffa solution and novel axiomatizations of the other three solutions. Hence, we provide a unified framework for comparing these solutions’ bargaining theories.Nash’s bargaining problem, robustness, intermediate agreements, the Discrete Raiffa solution, the Nash solution, the Kalai-Smorodinsky solution, Proportional solutions.