John Nash in 1950 gave an elegant solution to the bargaining problem using his somewhat controversial IIA axiom. Ehud Kalai and Meir Smorodinsky in 1975 gave a different solution replacing the IIA condition by their own Monotonicity condition. While the two solutions do not coincide in general, they obviously do so when the problem is symmetric. Are there other cases where the two solutions coincide? Indeed there are and we give a complete characterization.