Nash-in-Shapley: Bilateral Bargaining with Recursive Threat Points

33 Pages Posted: 7 Jan 2019 Last revised: 9 Jun 2019

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

We examine the role of competition and mergers in bargaining by embedding a performance game, in which retail prices are determined by competition, into an axiomatic bilateral bargaining model, in which suppliers and retailers negotiate wholesale terms. We prove existence and uniqueness of what we call the Nash-in-Shapley bargaining solution when threat points are built up recursively, from the set of agreements that would result absent each agreement. We compare and contrast outcomes to those in Nash-in-Nash and conclude Nash-in-Shapley is a useful addition to the competition toolbox, though when to use it depends, as always, on how well it captures significant features of competition.

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., Nash-in-Shapley: Bilateral Bargaining with Recursive Threat Points (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 )

401 21st Avenue South
Nashville, TN 37203
United States
615-322-9057 (Phone)
615-343-7177 (Fax)

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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