Pricing Information Cascades

We consider the problem of optimal pricing of a common-value
product in the presence of social learning effects. A new product
reaches the market and agents obtain private signals that partially
inform them about the value of this product. Agents decide
sequentially whether to purchase this product. Before making their own
decisions, they also observe the purchasing decisions of agents who
acted previously and learn from those actions in a Bayesian rational
fashion. We address the problem of how a firm should price the product
when taking social learning into account.

Our first result shows that firms do best asymptotically if the firms
select prices that lead the customers to learn the true value of the
product. We show how the firm can induce learning at a low cost by
inducing a vanishing fraction of the agents to act according to their
private signals. We also show a lower bound on the agents’ regret of
T^2/3 for a society of size T. We finally show a pricing policy
that achieves this lower bound.