A generalization of the Nash bargaining solution is defined for two-person bargaining problems with incomplete information. These solutions form the smallest set satisfying three axioms: a probability-invariance axiom, an extension (or independence of irrelevant alternatives) axiom, and a random-dictatorship axiom. A bargaining solution can also be characterized as an incentive-compatible mechanism that is both equitable and efficient in terms of some virtual utility scales for the two players.