Simulating mergers in a vertical supply chain with bargaining

Abstract

We model a two-level supply chain where Nash bargaining occurs upstream and firms compete in a logit setting downstream, either via Bertrand price setting or an auction. The parameters can be calibrated with a discrete set of data on prices, margins, and market shares, facilitating use by antitrust practitioners. We perform numerical simulations to identify cases where modelling the full vertical structure is important and where harm is likely. We also examine the thwarted Anthem/Cigna merger and show how the model weighs the various arguments made by the government and the defendants.

Modelling and predicting the competitive effects of vertical mergers: The bargaining leverage over rivals effect

“…Domnenko and Sibley (2019) extends Lu et al (2007) by numerically solving examples with asymmetric linear demand, again maintaining the assumption that upstream prices are determined before downstream prices. Sheu and Taragin (2017) considers the case that is the primary focus of this paper. It allows bargaining power to be split between the upstream and downstream firm and assumes that upstream and downstream prices are set simultaneously.…”

“…include Binmore et al (1986), Chipty andSynder (1999), Collard-Wexler et al (2019), Crawford et al (2018), Crawford and Yurukoglu (2012), Cuesta et al (2019), Dafny et al (2019), Das Varma andDe Stefano (2018), De Fontenay and Gans (2014), Domnenko andSibley (2019), Dragenska et al (2010), Gaudin (2018), Gowrisankaran et al (2015), Ho and Lee (2017), Iozzi and Valleti (2014), Nevo (2014) and Sheu and Taragin (2017).…”

“…In this case, the total surplus created by the exchange becomes fixed, and the negotiated input price affects only the split of a fixed amount of surplus between the parties. 5Moresi and Salop (2013) show how to construct such measures in the original RRC model.6 Other papers on vertically related markets that make the assumption that upstream and downstream prices are determined simultaneously includeCrawford et al (2018),Draganska et al (2010),Nocke and White (2007) andSheu and Taragin (2017).…”

Economics at the FTC: Estimating Harm from Deception and Analyzing Mergers

“…the incentive by the merged entity to raise its rivals' costs ("RRC"), and the incentive of the merged entity to expand its output owing to the elimination of double marginalization ("EDM"), see Sheu and Taragin (2021). Below, we discuss how the weighing of RRC and EDM effects differed in the context of NVIDIA/Arm, including nonstandard aspects of both elements.…”

Win/Loss Data and Consumer Switching Costs: Measuring Diversion Ratios and the Impact of Mergers*

“…We also do not account for any merger impacts on bargaining with upstream suppliers, which was another topic discussed extensively during the trial. Those vertical issues are examined inSheu and Taragin [2021]. In addition, our UPP measures do not account for any potential dynamic effects of the merger.© 2023 The Editorial Board of The Journal of Industrial Economics and John Wiley & Sons Ltd.…”