Pushing Notifications as Dynamic Information Design

We study the dynamic information design problem of a firm seeking to influence consumer checking behavior by designing push notifications. Firm payoffs are increasing in the frequency of consumer checking. The consumer is uncertain about the arrival of information as well as its valuation. In addition to direct consumption utility, the consumer also has preferences over realized uncertainty: she experiences disutility (anxiety) from the variance of the unchecked information stock. We show that push notifications can lead to more frequent checking compared to no-push, even though it reduces the information variance. While push notifications resolve the information arrival uncertainty, they also create an endogenous impulse to check the information immediately. They can allow the firm to create a more efficient spread in the consumer's beliefs/anxiety between zero or a level enough to induce checking. We generalize push strategies in two directions: a noisy push strategy that allows the firm to add phantom notifications and a partial push strategy in which the firm can mute information arrivals. Despite consumers having rational expectations, we establish conditions under which both these strategies increase checking. We also extend the model to account for consumer self-control as well as the possibility of endogenous prices