A Probabilistic Game‐Theoretic Method to Assess Deterrence and Defense Benefits of Security Systems

The U.S. Department of Homeland Security identifies deterrence as a key strategic priority. Nevertheless, no adequate method exists to quantify the deterrent effects of counterterrorism security systems (CTSSs). Game‐theoretic analyses of terrorism risk typically limit solutions to expected payoffs (EPs). This restricts the defender's ability to consider the full scope of outcomes and renders her vulnerable to the flaw of averages. The probabilistic game‐theoretic method (PGTM) is developed as an extension of game theory (GT) to explicitly account for uncertainties and remove the limitations of traditional decision‐making based solely on EPs. The problem of selecting robust optimal CTSSs under uncertainty is modeled as a Bayesian sequential defender–attacker game pictured in the form a hybrid decision‐game tree. The analysis uses Monte Carlo simulation and the results are reported as risk curves. The deterrent effects of CTSSs are endogenously determined. PGTM is applied to the problem of selecting an optimal CTSS for a small boat attack. The results demonstrate that PGTM can result in superior strategies than traditional GT that consider solely EPs and traditional probabilistic risk analyses of terrorism risk that do not account for deterrent effects because they do not endogenously model defender–attacker interactions.