We explore the constrained efficient observational learning model — as when individuals care about successors, or are so induced by an informationally-constrained social planner. We find that when the herding externality is correctly internalized in this fashion, in correct herds still obtain.
To describe behaviour in this model, we exhibit a set of indices that capture the privately estimated social value of every action. The optimal decision rule is simply: Choose the action with the highest index. While they have the flavour of Gittins indices, they also incorporate the potential to signal to successors. We then apply these indices to establish a key comparative static, that the set of stationary "cascade" beliefs strictly shrinks as the planner grows more patient. We also show how these indices yield a set of history-dependent transfer payments that decentralize the constrained social optimum.
The lead inspiration for the paper is our proof that information herding is but a special case of myopic single person experimentation. In other words, the incorrect herding outcome is not a new phenomenon, but rather just the familiar failure of complete learning in an optimal experimentation problem.