Heterogenity and Optimal Self-Reporting

We consider a model of optimal law enforcement according to which self-reporting may be considered in mitigation. After committing a crime, individuals get a private update of their probability of apprehension. Hence, self-enforcing has an option value of self-reporting, since criminals can decide whether or not to come forward after they have learned their types. We show that the optimal fine reduction is decreasing in the heterogeneity of the criminals' types if types are uniformly distributed. For general distribution functions, however, there are countervailing effects, which are discussed in a concluding section.