Recursive Nash-in-Nash bargaining solution

The standard Nash-in-Nash bargaining solution is commonly applied in a number of policy applications. However, the Nash-in-Nash framework does not capture renegotiations on off-equilibrium paths or contingent contracts, and as a result, in some situations the predictions of standard Nash-in-Nash are counterintuitive. 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. In the recursive Nash-in-Nash bargaining solution, the disagreement payoffs are the outcomes of bargaining with knowledge of the disagreement rather than the equilibrium outcomes as in the standard Nash-in-Nash. We show that under some assumptions, the recursive Nash-in-Nash bargaining solution is the same as the Shapley value for the corresponding game in characteristic function form or the more general Myerson value for the corresponding game in partition function form.