Information nudges and self-control

We study the optimal design of information nudges directed to present-biased consumers who make consumption decisions over time 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 fewer consumers have to be sacrificed, as they cannot be credibly warned even though they would like to be. Under a stronger present bias, 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 have a stronger present bias 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 that a health authority or a lobbyist would favor.