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