Abstract
© 2019 by The University of Chicago. All rights reserved. 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.
Published Version (Please cite this version)
10.1086/700729
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