Optimal Self-Reporting Schemes with Multiple Stages and Option Values

We consider a model of optimal law enforcement where sanctions can be reduced for self-reporting individuals. The literature is extended in two directions: First, we distinguish between two self-reporting stages: a first one before the case is investigated, and a second one where the criminal is detected but not yet convicted. Second, we assume that violators have private information in both stages. This leads to an option value of self-reporting, since criminals can decide whether to come forward or not after they have learned their types. We characterize the optimal policy and relate our results to self-reporting schemes observed in reality