| Abstract: | The presence of multiple sellers in the provision of (nonsubstitutable)complementary goods leads to outcomes that are worse than thosegenerated by a monopoly (with a vertically integrated productionof complements), a problem known in the economic literatureas complementary oligopoly and recently popularized in the legalliterature as the tragedy of the anticommons. We ask the followingquestion: how many substitutes for each complement are necessaryto render the presence of multiple sellers preferable to a monopoly?Highlighting the asymmetries between Cournot (quantity) andBertrand (price) competition and their dual models, we showthat the results crucially depend on whether firms compete bycontrolling price or quantity. Two substitutes per componentare sufficient when firms choose price. However, when firmschoose quantity, the availability of substitutes, regardlessof their number, is ineffective. Considering more complex casesof multi-complementarity, we ask the related question of howmany complements need to be substitutable and offer commentson equilibrium prices and quantities under different scenarios. |
