Optimal pricing in the presence of local network effects

Abstract

We study the optimal pricing strategies of a monopolist selling a divisible good (service) to consumers that are embedded in a social network. A key feature of our model is that consumers experience a (positive) local network e ffect. In particular, each consumer's usage level depends directly on the usage of her neighbors in the social network structure. Thus, the monopolist's optimal pricing strategy may involve o ffering discounts to certain agents3, who have a central position in the underlying network. Our results can be summarized as follows. First, we consider a setting where the monopolist can o er individualized prices and derive an explicit characterization of the optimal price for each consumer as a function of her network position. In particular, we show that it is optimal for the monopolist to charge each agent a price that is proportional to her Bonacich centrality in the social network. In the second part of the paper, we discuss the optimal strategy of a monopolist that can only choose a single uniform price for the good and derive an algorithm polynomial in the number of agents to compute such a price. Thirdly, we assume that the monopolist can o er the good in two prices, full and discounted, and study the problem of determining which set of consumers should be given the discount. We show that the problem is NP-hard, however we provide an explicit characterization of the set of agents that should be o ffered the discounted price. Finally, we describe an approximation algorithm for finding the optimal set of agents. We show that if the pro t is nonnegative under any feasible price allocation, the algorithm guarantees at least 88 % of the optimal pro fit.