  We develop a unified analysis of how information captures attention. A
decision maker (DM) observes a dynamic information structure and, at each
history, chooses between learning more and stopping to act. We show that all
feasible distributions over stopping times can be implemented by structures
such that, conditional on paying attention, the DM's beliefs follow a
deterministic path which makes her progressively more uncertain. We use this to
solve the problem of a designer with nonlinear preferences over DM's stopping
times: optimal structures have a {block structure} such that DM's indifference
times coincide with the support of her stopping time. Such structures
characterize extreme points of the set of feasible stopping times. We then show
designer-optimal structures always have {sequentially optimal} modifications
which eliminates the need for intertemporal commitment. We further characterize
designer-optimal structures when DM has noninstrumental value for information,
or when the designer values both attention and persuasion. Our results speak
directly to the attention economy.
