A security game model for environment protection in the presence of an alarm system

We propose, to the best of our knowledge, the first Security Game where a Defender is supported by a spatially uncertain alarm system which non-deterministically generates signals once a target is under attack. Spatial uncertainty is common when securing large environments, e.g., for wildlife protection. We show that finding the equilibrium for this game is FNP-hard even in the zero-sum case and we provide both an exact algorithm and a heuristic algorithm to deal with it. Without false positives and missed detections, the best patrolling strategy reduces to stay in a place, wait for a signal, and respond to it at best. This strategy is optimal even with non-negligible missed detection rates.