Abstract: Social media have become an increasingly important source of information about political, social and economic issues. While beneficial on many levels, the decentralized nature of these media may expose societies to novel risks of manipulation by third parties. To evaluate these risks, we study a model where a designer sends information to agents who interact in a game, so as to affect its outcome. The designer can communicate only with a limited number of agents, who then share information with each other on a network of social links before playing the game. We characterize the equilibrium outcomes that can be induced by seeding this social network with information. Our main result recasts this constrained information-design problem in terms of an equivalent linear program, which is particularly useful for applications. We show that a simple property of the network---the depth of communication---fully determines the scope for belief manipulation. Finally, we illustrate how a holistic use of linear-programming duality helps to characterize the solution to the optimal seeding problem. Our theory offers insights into the design of advertisement and political campaigns that are robust to (or leverage on) information spillovers.