Bring your friend! Real or virtual?

A monopolist faces a partially uninformed population of consumers, interconnected through a directed social network. In the network, the monopolist offers rewards to informed consumers (influencers) conditional on informing uninformed consumers (influenced). Rewards are needed to bear a communication cost. We find that social welfare always increases when the network becomes denser, but this may not be beneficial for the monopolist, who internalize transfers and may prefer an environment with less competition between informed consumers.