Search for a malevolent needle in a benign haystack
Glazebrook, K. D.
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A domain contains a number w of non-hostile White (W) individuals: humans, vehicles, ships. A hostile Red (R) individual enters the domain and travels through the domain towards targets. If R reaches an attractive valuable target, perhaps a crowd of people on land or a ship at sea containing liquid natural gas (LNG), it attacks the target. A Blue counter-terrorist, C, patrols the domain and classifies (perhaps incorrectly) individuals of interest as R or W. The probability of correct classification is an increasing function of the time spent classifying an individual. The misclassification of a W as an R is a false positive; misclassification of the R as a W is a false negative. C follows (or tracks) any individual it classifies as R until it is relieved by another platform or individual that may neutralize the possible R. C is unable to detect and classify additional individuals while it is following a suspicious individual. A small classification time may yield many false positives that C must service. A large classification time may result in R achieving its goal before being neutralized, so an appropriate compromise is sought. A game-theoretic model is formulated and studied to evaluate the probability that R is successfully neutralized before achieving its goal. C’s policy is to choose a classification time. Targets have independent identically distributed (iid) values, and R’s policy is to specify a target value threshold; R will attack the first target it finds whose value exceeds the threshold unless neutralized first.
Chapter 6 in Game Theoretic Risk Analysis of Security Threats (eds. Bier, V. M. and Azaiez, M. N.) International Series in Operations Research and Management Science, Vol. 128, Springer, New York, 2009.
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