TY - JOUR
T1 - “Nash-in-Nash” Bargaining
T2 - A Microfoundation for Applied Work
AU - Collard-Wexler, Allan
AU - Gowrisankaran, Gautam
AU - Lee, Robin S.
N1 - Funding Information:
This paper was previously circulated under the title “Bargaining in Bilateral Oligopoly: An Alternating Offers Representation of the ‘Nash-in-Nash’ Solution.” We would like to thank Elliot Lipnowski, Sebastián Fleitas, and Eli Liebman for excellent research assistance; Attila Ambrus, John Asker, Catherine de Fontenay, Joshua Gans, Patrick Greenlee, Heski Bar-Isaac, Rachel Kranton, Volcker Nocke, Janine Miklos-Thal, Dan O’Brien, Alexander Raskovich, Stan Reynolds, Mike Riordan, Chris Snyder, Mike Whinston, Tom Wiseman, Ali Yurukoglu, and numerous seminar audiences for useful discussion; and the editor and three anonymous referees for helpful comments. Gowrisankaran acknowledges funding from the National Science Foundation (grant SES-1425063). The usual disclaimer applies.
Publisher Copyright:
© 2019 by The University of Chicago. All rights reserved.
PY - 2019/2/1
Y1 - 2019/2/1
N2 - 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.
AB - 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.
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U2 - 10.1086/700729
DO - 10.1086/700729
M3 - Article
AN - SCOPUS:85059568786
SN - 0022-3808
VL - 127
SP - 163
EP - 195
JO - Journal of Political Economy
JF - Journal of Political Economy
IS - 1
ER -