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. We distinguish between a first self-reporting stage before the case is investigated and a second one where the criminal is detected, but not yet convicted. Since we assume that violators have private information in both stages, fine reductions for self-reporting individuals lead ceteris paribus to a higher violation frequency. Nevertheless, we show that fine reductions should be granted in both stages. We characterize the connection between the two fine reductions in the optimal policy and relate our results to self-reporting schemes observed in reality.