We consider a cross-calibration test of predictions by multiple potential experts in a stochastic environment. This test checks whether each expert is calibrated conditional on the predictions made by other experts. We show that this test is good in the sense that a true expert—one informed of the true distribution of the process—is guaranteed to pass the test no matter what the other potential experts do, and false experts will fail the test on all but a small (category I) set of true distributions. Furthermore, even when there is no true expert present, a test similar to cross-calibration cannot be simultaneously manipulated by multiple false experts, but at the cost of failing some true experts.

When an agent chooses between prospects, noise in information processing generates an effect akin to the winner's curse. Statistically unbiased perception systematically overvalues the chosen action because it fails to account for the possibility that noise is responsible for making the preferred action appear to be optimal. The optimal perception pattern exhibits a key feature of prospect theory, namely, overweighting of small probability events (and corresponding underweighting of high probability events). This bias arises to correct for the winner's curse effect. (JEL D11, D81, D82, D83)

We study the impact of manipulating the attention of a decision‐maker who learns sequentially about a number of items before making a choice. Under natural assumptions on the decision‐maker's strategy, directing attention toward one item increases its likelihood of being chosen regardless of its value. This result applies when the decision‐maker can reject all items in favor of an outside option with known value; if no outside option is available, the direction of the effect of manipulation depends on the value of the item. A similar result applies to manipulation of choices in bandit problems.

We solve a general class of dynamic rational-inattention problems in which an agent repeatedly acquires costly information about an evolving state and selects actions. The solution resembles the choice rule in a dynamic logit model, but it is biased towards an optimal default rule that does not depend on the realized state. We apply the general solution to the study of (i) the sunk-cost fallacy; (ii) inertia in actions leading to lagged adjustments to shocks; and (iii) the tradeoff between accuracy and delay in decision-making.

Participation payments are used in many transactions about which people know little but can learn more: incentives for medical trial participation, signing bonuses for job applicants, or price rebates on consumer durables. Who opts into the transaction when given such incentives? We theoretically and experimentally identify a composition effect whereby incentives disproportionately increase participation among those for whom learning is harder. Moreover, these individuals use less information to decide whether to participate, which makes disappointment more likely. The learning-based composition effect is stronger in settings in which information acquisition is more difficult.