Herd Design

The classic herding model examines the asymptotic behavior of agents who observe their predecessors' actions as well as a private signal from an exogenous information structure. In this paper we introduce a self-interested sender into the model, and study the sender's problem of designing this information structure. If agents cannot observe each other the model reduces to Bayesian persuasion. However, when agents observe predecessors' actions, they may learn from each other, potentially harming the sender. We identify necessary and sufficient conditions under which the sender can nevertheless obtain the same utility as when the agents are unable to observe each other.