Pricing negative externalities in social networks

We explore optimal monopoly pricing in the presence of local negative externalities among agents’ consumption. A monopolist first sets personalized prices, and consumers then simultaneously determine consumption levels. When network externalities are relatively small, the complement graph of the social network plays a key role in characterizing the equilibrium. Optimal prices are uniform when the production cost is linear and proportional to agents’ Katz-Bonacich centralities in the complement network when the production cost is convex. We further connect agents’ consumption with their degrees in several typical networks. The firm’s profit and total consumption decrease with network density, although the consumption of a specific agent may not decrease accordingly. Furthermore, in the context of directed networks, the monopolist charges higher prices to agents who generate substantial externalities for others without being reciprocally influenced. We also apply our model to the case involving large network externalities, where the monopolist exclusively sells products to consumers who constitute a maximum independent set.