Optimal Nonlinear Pricing in Social Networks under Asymmetric Network Information

We study the optimal nonlinear pricing of products and services in social networks, in which customers are strategic and their consumption exhibits local externality. Customers know about their local network characteristics (which are positively affiliated across neighbors), but the selling firm only has knowledge of the global network. We develop a solution approach based on calculus of variations and positive neighbor affiliation to tackle this nonstandard principal–agent problem faced by the firm. We show that the optimal pricing compromises the capitalization of the susceptibility to neighbor consumption with the motivation of one’s own consumption, which gives rise to a menu of quantity premium or quantity discount. In the Erdös and Rényi graph (a special case of the social network model we use), we find that the pricing scheme does not screen network positions; consequently, the firm can offer a simple uniform price. We conduct robustness checks of our results with two-way connections, in which the firm-optimal consumption becomes linear in customer degree in the scale-free network. Compared with linear pricing, we show that nonlinear pricing allows the firm to respond more effectively to the changes of network topology and economic factors.