Crime reporting: Profiling and neighbourhood observation

We consider the effect of giving incentives to ordinary citizens to report potential criminal activity. Additionally we look at the effect of 'profiling' and biased reporting. If police single out or profile a group for more investigation, then crime in the profiled group decreases. If a certain group is reported on more frequently through biased reporting by citizens, crime in the group reported on actually increases. In the second model, we consider a neighbourhood structure where individuals get information on possible criminal activity by neighbours on one side and decide whether to report or not based on the signal. When costs of reporting are low relative to the cost of being investigated, the costs of investigation increase in the number of reports and there is at least one biased individual. We show there is a "contagion equilibrium" where everyone reports his or her neighbour.