Recent technological advances have enabled firms to use data to price discriminate. This paper studies third-degree price discrimination (3PD) based on a random sample of valuation and covariate data, where the covariate is continuous, and the distribution of the data is unknown to the seller. The key assumption underlining the classic pricing theory is that the distribution of buyer valuations (and the covariate) is known to the seller. When a seller has only partial information about the distribution, how much revenue can be obtained then? In this paper, we assume that the seller has access to a random sample of i.i.d. {Yi, Xi}ni=1 drawn from FY,X, the joint distribution of the valuation Y and covariate X, and the seller does not know FY,X. The main results of this paper are twofold. The first set of results proposes a K-markets empirical revenue maximization (ERM) strategy. The second set of results is algorithm (pricing strategy) independent and reveals the fundamental information-theoretic limitation of any data-based pricing strategy.

We analyze screening with frame-dependent valuations. The optimal extensive form has a simple three-stage structure, using changes of framing (high-low-high) to induce dynamic inconsistency and thereby relax incentive compatibility constraints.

A sender seeks hard evidence to persuade a receiver to take a certain action. There is uncertainty about whether the sender obtains evidence. If she does, she can choose to disclose it or pretend to not have obtained it. When the probability of obtaining information is low, we show that the optimal evidence structure is a binary certification: all it reveals is whether the (continuous) state of the world is above or below a certain threshold. Moreover, the set of low states that are concealed is non-monotone in the probability of obtaining evidence. When binary structures are optimal, higher uncertainty leads to less pooling at the bottom because the sender uses binary certification to commit to disclose evidence more often.