Market Definition: A Sensitivity Analysis

TL;DR

This paper introduces a structured framework for sensitivity analysis in market definition using partial orders and graph representations, aiding antitrust analysts in assessing the robustness of their conclusions.

Contribution

It proposes a novel, organized approach employing Hasse diagrams and power indices to analyze market definition sensitivity in antitrust cases.

Findings

Effective visualization of market definition sensitivity.

Quantitative assessment of firms' influence on conclusions.

Application demonstrated on a real merger case.

Abstract

Market definition holds significant importance in antitrust cases, yet achieving consensus on the correct approach remains elusive. As a result, analysts routinely entertain multiple market definitions to ensure the resilience of their conclusions. I propose a simple framework for conducting organized sensitivity analysis with respect to market definition. I model candidate market definitions as partially ordered and use a Hasse diagram, a directed acyclic graph representing a finite partial order, to summarize the sensitivity analysis. I use the Shapley value and the Shapley-Shubik power index to quantify the average marginal contribution of each firm in driving the conclusion. I illustrate the method's usefulness with an application to the Albertsons/Safeway (2015) merger.