Who to share information with? Persuasion in social networks.

We study the information targeting and design problem of a sender in a setting where multiple receivers can communicate with each other through links in a social network. The sender commits to an information structure and chooses one of the receivers to initially observe the realised signal. The receivers simultaneously choose an action based on the information they possess, but are subject to peer effects. Each receiver wants her neighbours to choose the same action as her, and can strategically communicate her information to them. This triggers a strategic diffusion process through the network, with the realised signal reaching only a subset of receivers. The sender’s objective is to persuade as many receivers as possible to take a high action level. We characterise the optimal information and targeting strategy of the sender, highlighting the fundamental trade-off between information precision and extent of diffusion. Applications include political campaigns, lobbying, and raising participation in experimental settings. Contrary to common intuition, that targeting the “most central” agent in the network may not be optimal. The notion of centrality, which we term “influence” itself is endogenously determined by communication strategies and the information quality. We also conduct some comparative static analysis to understand how notions like homophily and network density affect the optimal policy of the sender.