Abstract
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 \(\mathcal {FNP}\)–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.
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Notes
- 1.
As is customary, we assume that \(\mathcal {A}\) can instantly reach the target of its attack. This assumption can be easily relaxed as shown in [3].
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Basilico, N., De Nittis, G., Gatti, N. (2015). A Security Game Model for Environment Protection in the Presence of an Alarm System. In: Khouzani, M., Panaousis, E., Theodorakopoulos, G. (eds) Decision and Game Theory for Security. GameSec 2015. Lecture Notes in Computer Science(), vol 9406. Springer, Cham. https://doi.org/10.1007/978-3-319-25594-1_11
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