Learning before trading: on the inefficiency of ignoring free information

This paper analyzes a bilateral trade model in which the buyer’s valuation for the object is uncertain and she can privately purchase any signal about her valuation. The seller makes a take-it-or-leave-it offer to the buyer. The cost of a signal is smooth and increasing in informativeness. We characterize the set of equilibria when learning is free, and show they are strongly Pareto ranked. Our main result is that when learning is costly but the cost of information goes to zero, equilibria converge to the worst free-learning equilibrium.