A new characterization of the non-symmetric Nash solution

A one-step stochastic bargaining procedure is examined which is based on assuming offer-dependent break-down probabilities and that at each step, the players optimize their expected payoffs. It is shown that there is a unique solution of the bargaining process and it reduces to the non-symmetric Nash solution if each player initially offers the disagreement payoff value to the other player. Therefore the one-step bargaining solution is a further generalization of the non-symmetric Nash solution with arbitrary initial offers.