Herding with costly information

This paper incorporates costly information into a model of observational learning. Individuals would like to avoid the cost of buying information and free-ride on the public history. The paper characterizes when learning is nevertheless complete. Necessary and sufficient conditions for complete learning follow from an elementary principle: a player purchases information only if it can influence her action. With a “coarse” action space, learning is complete if and only if for every cost c>0, a positive measure of types can acquire, at cost less than c, an experiment that can overturn the public history. With a “rich” action space, learning is complete if and only if for every cost c>0, a positive measure of types can acquire any informative signal at cost weakly less than c. The results are applied to financial markets to evaluate when markets are informationally efficient despite information being costly.