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

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  • Allan Collard-Wexler
  • Gautam Gowrisankaran
  • 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 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.

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  • Allan Collard-Wexler & Gautam Gowrisankaran & Robin S. Lee, 2014. "“Nash-in-Nash” Bargaining: A Microfoundation for Applied Work," NBER Working Papers 20641, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:20641
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    References listed on IDEAS

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    More about this item

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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