Substituting Complements

Abstract

The presence of multiple sellers in the provision of (non-substitutable) complementary goods leads to outcomes that are worse than those generated by a monopoly (with a vertically integrated production of complements), a problem known in the economic literature as complementary oligopoly and recently popularized in the legal literature as the tragedy of the anticommons. We ask the following question: how many substitutes for each complement are necessary to render the presence of multiple sellers preferable to a monopoly? Highlighting the asymmetries between Cournot (quantity) and Bertrand (price) competition and their dual models, we show that the results crucially depend on whether firms compete by controlling price or quantity. Two substitutes per component are sufficient when firms choose price. However, when firms choose quantity, the availability of substitutes, regardless of their number, is ineffective. Considering more complex cases of multi-complementarity, we ask the related question of how many complements need to be substitutable and offer comments on equilibrium prices and quantities under different scenarios.JEL classification: D43, D62, K11, L13.

Imperfect Substitutes for Perfect Complements: Solving the Anticommons Problem

“…Along the way, we will verify how the assumption of imperfect substitutability changes the impact of n on the extent of the tragedy of the anticommons when compared to the case studied by Dari‐Mattiacci and Parisi ()…”

“…As for welfare comparisons, we notice first from that, with a common quality value, no matter the extent of competition in sector B (i.e., no matter n ), ‘separating’ the two components of the system produced by an integrated monopolist and having them sold by two independent firms, always leads to higher prices. This clearly indicates that, when goods are not perfect substitutes, the tragedy of the anticommons is never solved by introducing competition in sector B , contrarily to what happens with perfect substitutes (Dari‐Mattiacci and Parisi, ) . In order to confirm such prediction, we now compare consumer surplus when sector B is an oligopoly with the one enjoyed under an integrated monopoly, establishing the following result…”

“…Investigating the impact of competition on welfare when complementary goods are involved, Dari‐Mattiacci and Parisi () note that, when n perfect complements are bought together by consumers and firms compete á la Bertrand, two perfect substitutes for n − 1 complements are sufficient to guarantee the same social welfare experienced when an integrated monopolist sells all n complements. In fact, all competitors in the n − 1 markets price at marginal cost, thus allowing the monopolist in the n ‐th market to extract the whole surplus, fixing its price equal to the one that would be set by an integrated monopolist for the composite good.…”

Complementary Platforms

“…the corresponding decrease in demand for the composite good D S ), will internalize the negative pricing externality exerted by individual producers and therefore set a lower, profit-maximizing bundle price (see e.g. Dari-Mattiacci and Parisi, 2006). As such, this is the horizontal equivalent of vertical integration to avoid the problem of double marginalization (Spengler, 1950).…”

Mergers with interfirm bundling: a case of pharmaceutical cocktails

“…Although the pricing of complements has been studied theoretically in various settings, there are few empirical analyses in the economic literature. Examples of theoretical treatments include Economides and Salop (), Economides (), Davis and Murphy (), Choi (), Dari‐Mattiacci and Parisi (), and Yan and Bandyopadhyay ().…”