A sender seeks hard evidence to persuade a receiver to accept a project by designing a quality test. Testing is not perfectly reliable and produces evidence only with some probability. If the sender obtains the evidence, she can choose to disclose it or pretend to not have obtained it. We show that when reliability is low, the sender chooses a pass/fail test that reveals whether the quality is above or below a threshold. Moreover, the equilibrium pass/fail threshold is always monotone in reliability but whether it is increasing or decreasing depends on whether evidence acquisition is overt or covert.

A sender commits to an experiment to persuade a receiver. Accounting for the sender’s experiment-choice incentives, and not presupposing a receiver tie-breaking rule when indifferent, we characterize when the sender’s equilibrium payoff is unique and so coincides with her “Bayesian persuasion” value. A sufficient condition in finite models is that every action which is receiver-optimal at some belief is uniquely optimal at some other belief—a generic property. We similarly show the equilibrium sender payoff is typically unique in ordered models. In an extension, we show uniqueness generates robustness to imperfect sender commitment.

The classic third degree price discrimination (3PD) model requires the knowledge of the distribution of buyer valuations and the covariate to set the price conditioned on the covariate. In terms of generating revenue, the classic result shows that 3PD is at least as good as uniform pricing. What if the seller has to set a price based only on a sample of observations from the underlying distribution? Is it still obvious that the seller should engage in 3PD? This paper sheds light on these fundamental questions. In particular, the comparison of the revenue performance between 3PD and uniform pricing is ambiguous overall when prices are set based on samples. This finding is in the nature of statistical learning under uncertainty: a curse of dimensionality, but also other small sample complications.

A principal faces an agent with frame-dependent preferences and designs an extensive-form decision problem with a frame at each stage. This allows the principal to induce dynamic inconsistency and thereby circumvent incentive compatibility constraints. We show that a vector of contracts can be implemented if and only if it can be implemented using a canonical extensive form, which has a simple high-low-high structure using only three stages and the two highest frames. We apply our results to the classic monopolistic screening problem. Some types buy in the first stage, while others continue the interaction and buy at the last stage. The firm offers unchosen decoy contracts. Sophisticated consumers correctly anticipate that if they deviated, they would choose a decoy, which they want to avoid in a lower frame. This eliminates incentive compatibility constraints into types who don’t buy in the first stage. With naive consumers, the principal can perfectly screen by cognitive type and extract full surplus from naifs.

With standard models of updating under ambiguity, new information may increase the amount of relevant ambiguity: the set of beliefs may ‘dilate.’ We experimentally test one sharp case: agents bet on a risky urn and get information that is truthful or not based on the draw from an Ellsberg urn. With common models, the set of beliefs dilates, and the value of bets decreases for ambiguity-averse agents and increases for ambiguity-seeking ones. Instead, we find that the value of bets does not change for ambiguity-averse individuals, while it increases substantially for ambiguity-seeking ones. We also test bets on ambiguous urns, in which case we find sizable reactions to ambiguous information.

A sender commissions a study to persuade a receiver, but influences the report with some probability. We show that increasing this probability can benefit the receiver and can lead to a discontinuous drop in the sender's payoffs. To derive our results, we geometrically characterize the sender's highest equilibrium payoff, which is based on the concavification of a capped value function.