Optimal influence design in networks

We examine an influence designer's optimal intervention in the presence of social learning in a network. Before learning begins, the designer alters initial opinions of agents within the network to shift their ultimate opinions to be as close as possible to the target opinions. By decomposing the influence matrix, which summarizes the learning structure, we transform the designer's problem into one with an orthogonal basis. This transformation allows us to characterize optimal interventions under complete information. We also demonstrate that even in cases where the designer has incomplete information about the network structure, the designer can still design an asymptotically optimal intervention in a large network. Finally, we provide examples and extensions, including repeated social learning and competition.