Attention Capture

A decision maker (DM) learns about an uncertain state via a dynamic information structure chosen by a designer and, at each history, optimally chooses between learning more and stopping to act. Thus, dynamic information structures induce joint distributions over outcomes (actions, states, and stopping times). We show there is no commitment gap: for arbitrary preferences over outcomes, designer-optimal structures can always be modified to be sequentially optimal. These modifications exploit the irreversibility of information to discipline the designer's future self. We then show all feasible distributions over outcomes are implementable with dynamic information structures for which stopping beliefs are extremal and continuation beliefs follow a deterministic path. We use these results to solve the problem of a designer with (i) 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; and (ii) preferences over actions and stopping times when they are additive or supermodular. Our results speak directly to the attention economy.