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In this paper, we present a new development of inspection games in a meanfield setting. In our dynamic version of an inspection game, there is oneinspector and a large number N interacting inspectees with a finite statespace. By applying the mean field game methodology, we present a solution as anepsilon-equilibrium to this type of inspection games, where epsilon goes to 0as N tends to infinity. In order to facilitate numerical analysis of this newtype inspection game, we conduct an approximation analysis, that is weapproximate the optimal Lipschitz continuous switching strategies by smoothswitching strategies. We show that any approximating smooth switching strategyis also an epsilon-equilibrium solution to the inspection game with a large andfinite number N of inspectees with epsilon being of order 1/N.

Inspection games in a mean field setting