Competitive pricing strategies in social networks

We study pricing strategies of competing firms who sell heterogeneous products to a group of customers in a social network. Goods are substitutes and each customer gains network externalities from her neighbors who consume the same products. We show that there is a unique subgame-perfect equilibrium where, first, firms choose the prices of each good for each consumer, and, then, individuals decide their consumption of the goods. We also fully characterize the equilibrium prices for any network structure, and relate these equilibrium outcomes to the familiar Katz-Bonacich network centrality measures. Contrary to the monopoly case, the equilibrium price of a customer not only depends on her own characteristics but also on others' characteristics. We show that firms price discriminate and charge lower prices to more central consumers. This means that more central consumers obtain a larger discount because of their impact in terms of consumption on their neighbors. We also show that the firms' equilibrium profits can decrease when either the network becomes denser or network effects are higher.