Inspection games in a mean field setting

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