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 $k$‐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.