🤖 AI Summary
Antitrust market definition lacks consensus, undermining the robustness of merger assessments. This paper proposes a systematic sensitivity analysis framework grounded in partially ordered sets (posets) and Hasse diagrams—the first application of Hasse diagrams to market definition research. Integrating Shapley values and the Shapley–Shubik power index, the method quantifies firms’ marginal contributions and power distributions across alternative market definitions. It enables interpretable, structured cross-definition evaluation, substantially enhancing analytical transparency and reproducibility. Applied to the 2015 Albertsons/Safeway merger case, the framework successfully identifies pivotal firms and assesses the robustness of market definitions under varying assumptions. The approach establishes a novel paradigm for antitrust economic analysis and delivers a practical, implementable tool for competition authorities and practitioners.
📝 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.