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

64 Pages Posted: 3 Nov 2014 Last revised: 26 Nov 2021

See all articles by Allan Collard-Wexler

Allan Collard-Wexler

Duke University

Gautam Gowrisankaran

Columbia University; HEC Montreal; Centre for Economic Policy Research (CEPR); National Bureau of Economic Research (NBER)

Robin S. Lee

Harvard University - Department of Economics; National Bureau of Economic Research (NBER)

Date Written: October 2014

Abstract

A “Nash equilibrium in Nash bargains” has become a workhorse bargaining model in applied analyses of bilateral oligopoly. This paper proposes a non-cooperative foundation for “Nash-in-Nash” bargaining that extends the Rubinstein (1982) 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”—i.e., 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.

Suggested Citation

Collard-Wexler, Allan and Gowrisankaran, Gautam and Lee, Robin S., “Nash-in-Nash” Bargaining: A Microfoundation for Applied Work (October 2014). NBER Working Paper No. w20641, Available at SSRN: https://ssrn.com/abstract=2518731

Allan Collard-Wexler (Contact Author)

Duke University ( email )

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Gautam Gowrisankaran

Columbia University ( email )

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Robin S. Lee

Harvard University - Department of Economics ( email )

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National Bureau of Economic Research (NBER) ( email )

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