Nash-in-Shapley: Bargaining with Recursive Threat Points
26 Pages Posted: 7 Jan 2019
Date Written: January 25, 2019
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: Suggested Citation