Bargaining Competition and Vertical Mergers

Abstract

A vertical merger model represents a complex system built on (i) a network of e.g., upstream manufacturers and downstream retailers (ii) who bargain bilaterally in the presence of externalities (iii) created by competition between downstream retailers (iv) facing a consumer demand surface. We simulate the effects of vertical mergers in six different bargaining models and and that how parties bargain, and over what, can almost pre-determine merger effects. This paper is accompanied by an online vertical merger simulator designed to help economists and enforcers simulate vertical mergers, similar to existing horizontal merger simulators. By showing what matters, why it matters, and how much it matters, these tools guide model building. We introduce the rectangular logit demand system for this application, with nests around the same goods sold at different retailers, or around different goods sold at the same retailer.

Keywords: Bargaining, Vertical Merger, Nash-in-Nash, Nash-in-Shapley, rectangular logit demand, nested logit demand.

JEL Classification: C78, D86, L14, L42