Recursive Nash-in-Nash Bargaining Solution

22 Pages Posted: 3 Feb 2019

See all articles by Xiaowei Yu

Xiaowei Yu

Bates White Economic Consulting

Keith Waehrer

Secretariat Economists

Date Written: January 20, 2018


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.

Keywords: Nash Bargaining, Nash-in-Nash, Shapley Value, Myerson Value

JEL Classification: L14, L40, C70

Suggested Citation

Yu, Xiaowei and Waehrer, Keith, Recursive Nash-in-Nash Bargaining Solution (January 20, 2018). Available at SSRN: or

Xiaowei Yu (Contact Author)

Bates White Economic Consulting

2001 K Street NW
North Building, Suite 500
Washington, DC 20006
United States

Keith Waehrer

Secretariat Economists ( email )

2121 K Street, NW
Suite 1100
Washington, DC 20037
United States
12024685646 (Phone)


Do you have negative results from your research you’d like to share?

Paper statistics

Abstract Views
PlumX Metrics