The standard Nash-in-Nash solution is commonly applied in a number of policy applications. However, this bargaining framework does not capture renegotiation on off-equilibrium paths or contingent contracts and as a result in some situations the predictions of standard Nash-in-Nash are counter-intuitive. Thus, we propose a new bargaining solution for interdependent bilateral negotiations, which we call the recursive Nash-in-Nash bargaining solution. The main difference between this bargaining framework and the standard Nash-in-Nash is in the treatment of the disagreement point, which we assume is the bargaining payoffs given that all other negotiations happen with recognition of this disagreement rather than the equilibrium outcomes. We show that under some assumptions, the recursive Nash-in-Nash bargaining solution is the same as the Shapley value or the more general Myerson value for the corresponding cooperative game. This equivalence allows the recursive Nash-in-Nash solution to be calculated relatively easily for policy applications.