A new, more fundamental approach is proposed to the classical bargaining problem. The give-and-take feature in the negotiation process is explicitly modelled under the new framework. A compromise set consists of all allocations a player is willing to accept as agreement. We focus on the relationship between the rationality principles (arguments) adopted by players in making mutual concessions and the formation of compromise sets. The bargaining correspondence is then defined as the intersection of players’ compromise sets. We study the non-emptiness, symmetry, efficiency and single-valuedness of the bargaining correspondence, and establish its connection to the Nash solution. Our framework provides a rational foundation to Nash’s axiomatic approach.