Mixed markets and crime

This paper specifies and solves a two-stage, game theoretic model of a mixed market for crime control. In the first stage of the model, private targets and the government choose levels of policing. In the second stage, criminals choose targets and the severity of the crimes that they commit.The paper's key results are as follows. First, private policing can both divert crime to targets that lack private protection and also increase the severity of the crime that these less-protected targets suffer. Second, an increase in private policing reduces the aggregate expenditure on traditional policing. This is an instance of a political incentive externality, where private policing affects the objective function of the government. Specifically, it reduces the level of traditional policing that is consistent with the Samuelson condition for efficient provision of a public good. Third, the substitution of private for public policing carries with it a change in the technology of policing. In effect, private policing leads to a shift from enforcement and punishment towards monitoring and target hardening. This, in turn, may lead to an increase in the severity of crime. Fourth, the mixed policing equilibrium is inefficient, and, in some situations, mixing may reduce the utility of all targets.