Optimal policing with (and without) criminal search

We develop a search-theoretic model, in which a police agency allocates scarce resources across neighborhoods—heterogeneous in “vigilance” and valuables—to minimize crime, while potential criminals decide whether, and if so, when and where to commit a crime. When criminals sequentially search for the best target, the optimal police allocation depends on the difference in vigilance levels across neighborhoods, prioritizing neighborhoods with low vigilance. However, in the absence of criminal search, the optimal allocation depends on the degree of rent inequality among neighborhoods, with a priority placed on neighborhoods with higher rents. We also identify conditions under which policing all neighborhoods equally is optimal. Our findings underscore that an optimal policing design must not only consider neighborhood characteristics but also other factors that may impact criminals’ decision-making, including whether they engage in active search.