Information Nudges and Self-Control

We study the optimal design of information nudges for present-biased consumers who make sequential consumption decisions without exact prior knowledge of their long-term consequences. For any distribution of risks, there exists a consumer-optimal information nudge that is of cutoff type, recommending abstinence if the risk is high enough. Depending on the distribution of risks, more or less consumers have to be sacrificed, as they cannot be credibly warned even though they would like to be. Under a stronger bias for the present, the target group receiving a credible warning to abstain must be tightened, but this need not increase the probability of harmful consumption. If some consumers are more strongly present-biased than others, traffic-light nudges turn out to be optimal and, when subgroups of consumers differ sufficiently, the optimal traffic-light nudge is also subgroup-optimal. We finally compare the consumer-optimal nudge with those a health authority or a lobbyist would favor.