Nash-in-Shapley: Bargaining with Recursive Threat Points

26 Pages Posted: 7 Jan 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: January 25, 2019

Abstract

We examine the role of competition in bargaining by embedding a performance game in which retail prices are determined by competition, into a bargaining game where suppliers and retailers negotiate wholesale terms. In a perfect information game, we prove existence and uniqueness of what we call the Nash-in-Shapley bargaining outcome when threat points are built up recursively, from the set of agreements that would result absent each agreement. We find that seemingly innocuous assumptions, i.e., contingent contracts and two-part pricing, eliminate competition in the performance game for parties that are linked by a chain of agreements. We compare and contrast outcomes to those in Nash-in-Nash to better understand how mergers affect 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: Bargaining with Recursive Threat Points (January 25, 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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