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Inspection games with long-run inspectors

The inspection game has been widely used as a model for crime deterrence. In this article, we shall present a broad review of the literature and an original result. The original result concerns the interaction between a single, long-run inspector and a population of short-run, boundedly rational would-be criminals. This approach gives rise to an optimal control problem that can be solved explicitly. We show that a forward-looking inspector obtains the same payoff he would obtain if he could commit to a probability of inspection. The consequences of this result for the economics of crime deterrence are also explored.