“Nash-in-Nash” Bargaining: A Microfoundation for Applied Work

Friday, January 4, 2019
Allan Collard-Wexler, Gautam Gowrisankaran, and Robin S. Lee

Abstract

A “Nash equilibrium in Nash bargains” has become a workhorse bargaining model in applied analyses of bilateral oligopoly. This paper proposes a noncooperative foundation for “Nash-in-Nash” bargaining that extends Rubinstein’s alternating offers model to multiple upstream and downstream firms. We provide conditions on firms’ marginal contributions under which there exists, for sufficiently short time between offers, an equilibrium with agreement among all firms at prices arbitrarily close to Nash-in-Nash prices, that is, each pair’s Nash bargaining solution given agreement by all other pairs. Conditioning on equilibria without delayed agreement, limiting prices are unique. Unconditionally, they are unique under stronger assumptions.

Citation: 

Allan Collard-Wexler, Gautam Gowrisankaran, and Robin S. Lee, "“Nash-in-Nash” Bargaining: A Microfoundation for Applied Work," Journal of Political Economy 127, no. 1 (February 2019): 163-195. https://doi.org/10.1086/700729

Journal of Political Economy