Statistical criteria for sequential inspector-leadership games

This paper considers ways of modelling time dependent inspection problems where there is a possibility of false alarms. For this purpose, it is assumed that safeguards procedures are notified to the inspectee by the inspector and are prima facie plausible ones. This ‘inspector-leadership principle’ implies that under reasonable assumptions the inspectee’s strategy is legal in the sense of complying with agreed rules. The main objective of our investigation is to derive simple criteria for the determination of optimal inspection procedures from the equilibrium conditions for non-cooperative non-zero sum two-person games. It can be shown that, given the appropriate assumptions, one can arrive at ‘statistical’ optimization criteria. In the simplest case one gets the global probabilities of the errors of the first and second kind and in more complex cases the average run lengths for legal and illegal inspectee behavior.