Optimal pricing in social networks

Abstract

We consider the pricing strategies of a monopolist selling a divisible good (service) to consumers who are embedded in a social network. We assume that each consumer's usage level depends directly on the usage of her neighbors in the social network, and investigate the optimal pricing policies of the monopolist. We show that if the monopolist can perfectly price discriminate the agents, then the price offered to each agent has three components: a nominal price, a discount term due to the agent's influence on her neighbors, and a markup term due to the influence of her neighbors on the agent. We also characterize the optimal pricing strategies in settings where the monopolist is constrained to offering a single price, and where she can choose two distinct prices (a discounted and a full price). For the former setting we provide a polynomial time algorithm for the solution of the pricing problem. On the other hand, we show that in the latter setting the optimal pricing problem is NP-hard, and we provide an approximation algorithm, which, under some conditions, achieves at least 88% of the maximum profit.