The probability to reach an agreement as a foundation for axiomatic bargaining

We revisit the Nash bargaining model and axiomatize a procedural solution that maximizes the probability of successful bargaining. This probability-based approach nests both the standard and the ordinal Nash solution, and yet need not assume that bargainers have preferences over lotteries or that choice sets are convex. We consider both mediator-assisted bargaining and standard unassisted bargaining. We solve a long-standing puzzle and offer a natural interpretation of the product operator underlying the Nash solution. We characterize other known solution concepts, including the egalitarian and the utilitarian solutions.