Decision makers conducting costly experiments often seek advice from experts with a stake in the outcome: executives evaluating competing product designs or policymakers designing new regulation consult specialized engineers or industry lobbyists who have frontier expertise. I study how a decision maker experimenting across multiple prospects may interact productively with a biased expert who strategically discloses verifiable evidence about each prospect. The expert favors a subset of prospects, regardless of their viability for the decision maker, and neither player can commit to future behavior. The order of experimentation shapes the expert's incentives: testing favored prospects earlier can induce disclosure about alternatives if experimentation continues. Pareto-efficient equilibria feature disclosure in batches, generally with delay. Between disclosures, the decision maker experiments optimally according to an adjusted Gittins index. Under refinements that rule out implausible disclosure behavior, optimal experimentation follows an endogenous index ordering across all prospects. Comparative statics highlight that faster learning or greater alignment with the expert need not improve the decision maker's welfare.

We study Poisson bandit problems in which a decision maker chooses which project to exploit, which projects to explore, and whether to seek good or bad news about each. We identify an Immediate Actionability Principle: an optimal policy seeks bad news about the exploited project or good news about alternatives, both directed at immediately changing current exploitation. The principle holds in every environment with two projects, for arbitrary correlation. With many projects, we identify conditions supporting sequential elimination, sequential upgrading, and dispersed good-news search. Sequential elimination is optimal for mutually exclusive successes and exchangeable states, and under additional ranking conditions for independent and common-factor projects. The principle can fail in either direction because a revelation can be valuable through its effect on subsequent exploration. Finally, with equal rewards, exchangeable states, and full disentanglement, the worst-case loss from fixing news compositions in advance is equivalent to halving the attention budget.

Centralized matching markets involve many participants operating under limited information about others' preferences and priority rankings. This paper adopts a robust approach to imperfect information, analyzing worst-case outcomes for applicants in the deferred acceptance mechanism. In a setting where applicants' preferences are IID uniform, I characterize the probability that an applicant can secure a guaranteed outcome, independent of positions' priority over applicants. The probability that an applicant can guarantee his kth favorite position declines exponentially with both k and market size, leading to the asymptotic failure of percentile guarantees. These results highlight potential limits on applicants' participation incentives. The proof connects weak guarantees to the prevalence of perfect matchings in random markets. I further demonstrate that correlated applicant preference rankings hamper guarantees, while anti-correlated rankings improve guarantees. Finally, I explore how constraining positions' priority structures may enhance outcomes.

We study efficient deterrence when agents are ambiguity averse. We show that a principal can implement deterrence more efficiently by obfuscating over conditional punishments associated with each level of compliance. However, obfuscation introduces endogenous limits to the range of outcomes the principal can achieve: perceived consequences depend on observable rates of compliance, which in turn result from agents' perceptions. We characterize the set of perceived consequences obfuscation can sustain: crucially, the perception of harsh consequences for severe non-compliance requires a critical mass of partial compliers. Under an obfuscated policy, the principal has reduced flexibility over how agents perceive differences in consequences across levels of non-compliance. We derive sufficient conditions for when the principal prefers obfuscation versus transparency. A principal may prefer transparency when the marginal effort of partial compliance is so costly that obfuscation cannot sustain a perceived gap between partial compliance and severe non-compliance large enough to deter the latter.