Abstract
This paper reconsiders the problem of optimal law enforcement when the apprehension probability depends on the offense rate as well as policing expenditures. A natural consequence of such an apprehension probability is the possible multiplicity of the equilibrium due to strategic complementarity, and the actual offense rate is realized by the self-fulfilling nature of the offense rate. If people believe that lowering the fine will lead to a lower offense rate, each individual will be less inclined to commit an illegal activity due to their expectation of a higher apprehension probability. Thus, the maximal fine is not socially optimal in this case.
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