Persuasion in Networks With Strategic Substitutes

We study Bayesian persuasion with local strategic substitutes in networks. A designer commits to a public signal to maximize total activity. Equilibria are characterized by the network's maximum $k$-insulated sets for each realization. We solve the optimal information structure and characterize beneficial persuasion. While agents individually prefer higher states, the designer's payoff is non-monotonic in the posterior mean due to substitution effects. This provides a rationale for downwardplaying mechanisms: revealing low states truthfully and mixing signals when high. Moreover, for tree, nested split, and core-periphery networks, the designer strictly benefits if the prior mean insulated set size is less than the highest state set size.