Optimal Sequential Allocation with Imperfect Feedback Information

Abstract

A given number of bullets will be fired sequentially in an attempt to destroy as many targets as possible from a fixed number of targets. The probability of destroying a target at each shot is known. After each shot, there is a report on the state for the target; destroyed or intact. The reports are subject to the usual two types of errors and the probabilities of making these errors are also known. This paper shows that the myopic decision strategy that picks the next target to be the one with the highest intact posterior probability is the optimal strategy.