How informed do you want your principal to be?

Résumé

We study a bilateral trade setting with interdependent values and two-sided private information. A buyer’s value for a good depends both on his privately known type and the good’s quality that he does not observe. The cost of the seller also depends on both the buyer’s type and the quality; she learns about the latter via a private signal whose realization is the seller’s private information. How much (if any) private information would the buyer want the seller to have? We answer this question by characterizing the buyer-optimal outcome: this is the information structure and the corresponding seller-optimal equilibrium of the informed principal game that yield the highest consumer surplus. We show that, and characterize precisely when, private information for the seller leads to higher consumer surplus relative to an uninformed seller. Under these conditions, the information structure in the buyer-optimal outcome is typically noisy. (joint with Rahul Deb and Mallesh Pai)