Two firms engage in price competition to attract buyers located on a network. The value of the good of either firm to any buyer depends on the number of neighbors on the network who adopt the same good. When the size of externalities increases linearly with the number of adoptions, we identify the set of price strategies that are consistent with an equilibrium in which one of the firms monopolizes the market. The set includes marginal cost pricing as well as bipartition pricing, which offers discounts to some buyers and charges markups to others. We show that marginal cost pricing fails to be an equilibrium under non-linear externalities but identify conditions for an equilibrium with bipartition pricing to be robust against perturbations in the externalities from linearity. The idea of bipartition pricing is then applied to the analysis of platform competition in a two-sided market under local and approximately linear externalities.
graphs divide and conquer price discrimination two-sided markets partition