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 sufficiently low, the equilibrium evidence structure is a pass/fail test: all it reveals is whether the (continuous) state of the world is above or below a certain threshold. Moreover, in this case the equilibrium pass/fail threshold is always monotone in reliability but whether it is increasing or decreasing depends on whether the sender’s acquisition is overt or covert.

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.

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. We also examine a public-persuasion setting, where we observe the report’s susceptibility to influence restricts the amount of information the sender can provide. To derive our results, we geometrically characterize the sender’s highest equilibrium payoff, which is based on the concave envelope of her capped value function.

A sender publicly commits to an experiment to inform a receiver’s decision. We study attainable sender payoffs, accounting for her incentives at the experiment choice stage, and not presupposing a receiver tie-breaking rule when indifferent. We characterize when the sender has a unique equilibrium payoff, which therefore coincides with her optimal value in Kamenica and Gentzkow (2011). A sufficient condition is that every action which is a receiver best response to some belief over a set of states is a unique best response to some other such belief—a generic property in the finite case.

With standard models of updating under ambiguity, new information may increase the amount of relevant ambiguity: the set of priors may `dilate.' We test experimentally 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 priors should dilate, and the value of bets decrease for ambiguity-averse individuals, increase if ambiguity-seeking. Instead, we find that the value of bets does not change for ambiguity-averse agents; it increases substantially for ambiguity-seeking ones. We also test bets on ambiguous urns and find sizable reactions to ambiguous information.