Modeling Bargaining Competition: Nash-in-Shapley vs. Nash-in-Nash

16 Pages Posted: 7 Jan 2019 Last revised: 27 Jan 2021

See all articles by Luke M. Froeb

Luke M. Froeb

Vanderbilt University - Owen Graduate School of Management

Vlad Mares

INSEAD

Steven Tschantz

Vanderbilt University - Department of Mathematics

Date Written: June 7, 2019

Abstract

In this paper, we document two shortcomings of Nash-in-Nash bargaining: outcomes depend on who earns operating profit (a violation of the Coase Theorem); and "schizophrenia," parties behaving "as if" they were bargaining against themselves. Schizophrenia makes makes the pre-merger equilibrium more competitive, and mergers more anti-competitive, than the "Nash-in-Shapley" alternative in which firms bargain in recognition of how their bargains affect final imputations. We find that even when parties bargain bilaterally and independently, they reach cooperative outcomes if they are linked by a chain of bilateral agreements.

Keywords: Bargaining, Contingent Contracts, Nash-in-Shapley, Nash-in-Nash, Vertical and Horizontal Mergers

JEL Classification: C78, D86, L14, L41, L42, G34

Suggested Citation

Froeb, Luke M. and Mares, Vladimir and Tschantz, Steven T., Modeling Bargaining Competition: Nash-in-Shapley vs. Nash-in-Nash (June 7, 2019). Available at SSRN: https://ssrn.com/abstract=3304179 or http://dx.doi.org/10.2139/ssrn.3304179

Luke M. Froeb (Contact Author)

Vanderbilt University - Owen Graduate School of Management ( email )

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615-322-9057 (Phone)
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Vladimir Mares

INSEAD ( email )

Boulevard de Constance
77305 Fontainebleau Cedex
France

Steven T. Tschantz

Vanderbilt University - Department of Mathematics ( email )

Nashville, TN 37240
United States

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