Pushing Information: Realized Uncertainty and Notification Design

We study the dynamic information design problem of a firm seeking to influence consumer checking behavior. The firm's payoffs increase in the frequency of consumer checking, and it can design push notifications to induce 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 information stock that has arrived, but which remains unchecked. We show that push notifications can lead to more frequent checking compared to no-push, even though it reduces the variance of the information. While push notifications resolve the information arrival uncertainty, they also create an endogenous impulse to check the information immediately. They may 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 consider generalized push strategies that allow the firm to strategically add phantom notifications that do not contain useful information. This noisy push strategy can lead to more frequent consumer checking, even though the consumer has rational expectations about the firm's strategy. We extend the model to account for consumer self-control to show that sophisticated consumers have the equilibrium incentive to block notifications. The main results also hold in a model with endogenous prices.