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On the Role of Bargaining Power in Nash-in-Nash Bargaining: When More is Less

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Abstract
In bargainings, the parties’ bargaining powers (BPs) may determine not only how the surplus is shared (share effect), but also the size of the aggregate surplus (size effect). Since the size effect may be positive or negative, the sign of the effect on a party’s payoff of a change in her BP is in principle undetermined. We first look at a general model with a party (the principal) negotiating with two counterparts. At the Nash-in-Nash solution, we show that the equilibrium payoff of the principal may be decreasing in her BP. Necessary conditions for this to occur are an asymmetric bargaining model and a sufficiently large difference in the way the bargained upon variables affect the principal’s payoff. We then revisit a standard linear vertical industry with one upstream firm, downstream Cournot competition, and public contracts. A negative effect on the upstream firm’s profits deriving from an increase in her BP is always found when the firm has different BPs across the negotiations and final goods are complements. We map these conditions to those characterised in the general model.

Suggested Citation

  • Marc Escrihuela-Villar & Walter Ferrarese & Alberto Iozzi, 2022. "On the Role of Bargaining Power in Nash-in-Nash Bargaining: When More is Less," CEIS Research Paper 550, Tor Vergata University, CEIS, revised 22 Dec 2022.
    • Handle: RePEc:rtv:ceisrp:550
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    References listed on IDEAS

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    1. Michaela Draganska & Daniel Klapper & Sofia B. Villas-Boas, 2010. "A Larger Slice or a Larger Pie? An Empirical Investigation of Bargaining Power in the Distribution Channel," Marketing Science, INFORMS, vol. 29(1), pages 57-74, 01-02.
    2. Matthew Grennan, 2013. "Price Discrimination and Bargaining: Empirical Evidence from Medical Devices," American Economic Review, American Economic Association, vol. 103(1), pages 145-177, February.
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    More about this item

    Keywords

    bargaining power; Nash-in-Nash; vertical relations;
    All these keywords.

    JEL classification:

    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law

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