Nash's bargaining solution when the disagreement point is random

In his seminal work, Nash (1950) [Nash, J.F. (1950). “The Bargaining Problem”, Econometrica, 18, 155-162.] derives a solution for two-person bargaining problems, within a cooperative setup. Nash assumes that the result of disagreement is known to both players and is not stochastic. We study the same problem, where the last assumption is relaxed. We provide a set of axioms which characterizes a natural generalization of the Nash solution to bargaining problems with a random point of disagreement.