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We study the optimal referral strategy of a seller and its relationship withthe type of communication channels among consumers. The seller faces apartially uninformed population of consumers, interconnected through a directedsocial network. In the network, the seller offers rewards to informed consumers(influencers) conditional on inducing purchases by uninformed consumers(influenced). Rewards are needed to bear a communication cost and to induceword-of-mouth (WOM) either privately (cost-per-contact) or publicly (fixed costto inform all friends). From the seller's viewpoint, eliciting Private WOM ismore costly than eliciting Public WOM. We investigate (i) the incentives forthe seller to move to a denser network, inducing either Private or Public WOMand (ii) the optimal mix between the two types of communication. A densernetwork is found to be always better, not only for information diffusion butalso for seller's profits, as long as Private WOM is concerned. Differently,under Public WOM, the seller may prefer an environment with less competitionbetween informed consumers and the presence of highly connected influencers(hubs) is the main driver to make network density beneficial to profits. Whenthe seller is able to discriminate between Private and Public WOM, the optimalstrategy is to cheaply incentivize the more connected people to pass on theinformation publicly and then offer a high bonus for Private WOM.

Bring a friend! Privately or Publicly?