On the Inspection Game

Thomas S. Ferguson and Costis Melolidakis


We treat the following two-person zero-sum game between the inspector and the smuggler, defined by the parameters n, m, k, and q. The smuggler has m truckloads of toxic waste that she would like to dispose of. There is no cost to her for dumping a truckload of toxic waste in the river unless she gets caught by the inspector, in which case she loses +1 each time she is caught. Instead she may dispose of any truckload herself in a legal way at a cost of q per truckload, where q is in the interval [0,1]. However, after n days, the inspector will inspect her homebase and force her to dispose legally of any waste he finds there. In the meantime, she may try to dump one truckload in the river each day. But the inspector only has staff enough to watch her on k of those days.