Working Paper No. 05-25:
Substituting Complements

Author(s):

Giuseppe Dari-Mattiacci, Francesco Parisi

Date Posted: 2005

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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 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 2 substitutes per component are sufficient. 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.