Implied Market Shares and Antitrust Markets as Fuzzy Sets

Abstract

Market definition is an important aspect of antitrust analysis, but the exercise requires designating each potentially relevant good as either completely in or out of the market. In a market with differentiated goods, this often necessitates making unsatisfactory designations. This article introduces the concept of the antitrust market as a fuzzy set, where each relevant good can have a degree of membership in the market, rather than only the traditional binary in or out designation. A product’s degree of membership in the market is assigned based on its closeness of substitutability to the focal products. We then show how implied market shares can be calculated from a defined fuzzy antitrust market. We illustrate an implementation of these concepts using data from the grocery retail market and demand estimations from prior literature. We also discuss how this concept serves as a middle way between supporters and detractors of market definition, as implied market shares are objects that not only reflect demand substitutability but also allow for the rhetorical benefits of having delineated a market to focus discussion and analysis of competitive issues.