Imperfect Substitutes for Perfect Complements: Solving the Anticommons Problem

Abstract

An integrated monopoly, where all complements forming a composite good are oered by a single rm, is typically welfare superior to a complementary monopoly. This is the tragedy of the anticommons. We consider the possibility of competition in the market for each complement. We present a model with two perfect complements and introduce n imperfect substitutes for one and then for both complements. We prove that, if one complementary good is produced by a monopolist, and if competition for the other complement does not vary the average quality in the market, then an integrated monopoly is still superior. In such case, favoring competition in some sectors, leaving monopolies in others would be detrimental for consumers and producers alike. Competition may be preferred if and only if the substitutes of the complementary good dier in their quality, so that as their number increases, average quality and/or quality variance increases. Results change when competition is introduced in each sector. In this case, if goods are close substitutes, we nd that competition may be welfare superior for a relatively small number of competing rms in each sector, even with no quality dierentiation. JEL Codes: D43, D62, K11, L13.

Introduction: opportunities and challenges of the digital single market

“…It is evident, therefore, that the analysis of competition among platforms is complex and has to consider many different aspects. A crucial aspect is that of the "tragedy of the anticommons," generated by complementarity (Michelman, 1982;Heller, 1998;Dari-Mattiacci and Parisi, 2006;Alvisi and Carbonara, 2013). Starting from the scenario presented by Cournot (1838) in his "complementary monopoly"-in which two companies are monopolists in the production of two goods (one for each company) that are complement inputs in the production of a third composite good-the tragedy of the anticommons lies in the fact that welfare in this industry decreases with the number of individual producers.…”

Digital platforms, multi-sided markets, and the anticommon problem

“…Integration has no impact on social welfare, and the prescription for antitrust authorities would be inactivity (i.e., maintaining the existing market configuration, be that integrated or separated firms). Alvisi and Carbonara (2013) proved instead that these conclusions change significantly when the assumption of perfect substitutability is relaxed, and the components are produced in an oligopolistic setting with product differentiation. They studied a case of a composite good consisting of two perfectly complementary components.…”