Extension of a Model for Timely Inspection

A number of years ago Diamond derived a general solution for the problem of determining a randomized inspection strategy which optimizes the time to detection on a reference interval. In his model, Diamond assumed 100% detection probability and no possibility of false alarms for the interim inspections, and also that the inspectee will behave illegally with 100% probability. These assumptions were consistent with modelling the problem as a zero-sum game with time to detection as payoff to the inspectee. In the context of a nuclear safeguards inspection regime, it is desirable to allow for detection probabilities that are less than 100% and for the possibility of false alarms. Since false alarms are disadvantageous for both parties, the zero-sum assumption is then no longer tenable. Moreover, the alternative of legal behavior on the part of the inspectee likewise cannot be treated within a zero-sum game model. In our contribution, therefore, we formulate a general non-cooperative game between inspector and inspectee in which the players' utilities reflect their priorities over a reference time interval. The inspector prefers deterrence (that is, legal behavior on the part of the inspectee) to detection of violation; the inspectee prefers illegal behavior if he is not detected, and both protagonists wish to avoid false alarms. As in Diamond's original formulation, it is assumed that the inspectee decides on his strategy in advance. Solutions are presented for the cases of one and two interim inspections. Unlike analogous sequential game models, the solutions prescribe randomization both of the inspection and violation times. The results will be interpreted within the context of current discussions of unannounced random inspections under the extended Safeguards Protocol