Self-Reporting and Ex Post Asymmetric Information

We consider a model of optimal law enforcement where sanctions are reduced for self-reporting individuals. Violators get private signals about their individual probabilities of apprehension after they committed a crime. Since violators will self-report if and only if the signal is above a specific threshold, the possibility of self-reporting has an option value that leads to a higher crime rate if the authority's effort remains unchanged. We demonstrate that self-reporting nevertheless increases social welfare even under the restriction that the crime rate must not be higher than without self-reporting.