Substituting Complements

18 Pages Posted: 13 Sep 2005 Last revised: 1 Apr 2011

See all articles by Giuseppe Dari‐Mattiacci

Giuseppe Dari‐Mattiacci

University of Amsterdam; Tinbergen Institute; European Corporate Governance Institute (ECGI)

Francesco Parisi

University of Minnesota - Law School; University of Bologna; University of Miami, School of Law

Multiple version iconThere are 2 versions of this paper

Date Written: 2006


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 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 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.

Keywords: Anticommons, complementary inputs, oligopoly, antitrust, competition

JEL Classification: D43, D62, K11, L13

Suggested Citation

Dari-Mattiacci, Giuseppe and Parisi, Francesco, Substituting Complements (2006). Journal of Competition Law and Economics, Vol. 2, No. 3, pp. 333-347, 2006, George Mason Law & Economics Research Paper No. 05-25, Minnesota Legal Studies Research Paper No. 07-13, Amsterdam Center for Law & Economics Working Paper No. 2005-04, Available at SSRN:

Giuseppe Dari-Mattiacci (Contact Author)

University of Amsterdam ( email )

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Amsterdam, Noord-Holland 1001 ND

Tinbergen Institute ( email )

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European Corporate Governance Institute (ECGI) ( email )

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Francesco Parisi

University of Minnesota - Law School ( email )

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Minneapolis, MN 55455
United States

University of Bologna ( email )

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40126 Bologna, fc 47100

University of Miami, School of Law ( email )

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