Multiple agents finitely repeated inspection game with dismissals

This paper deals with an inspection game between a single inspector and several independent (potential) violators over a finite-time horizon. In each period, the inspector gets a renewable inspection resource, which cannot be saved and used in future periods. The inspector allocates it to inspect the (potential) violators. Each violator decides in each period whether to violate or not, and in what probability. A violation may be detected by the inspector with a known and positive probability. When a violation is detected, the responsible violator is “dismissed” from the game. The game terminates when all the violators are detected or when there are no more remaining periods. An efficient method to compute a Nash equilibrium for this game is developed, for any possible value of the (nominal) detection probability. The solution of the game shows that the violators always maintain their detection probability below 0.5.