Giuseppe De Nittis

Adversarial patrolling with spatially uncertain alarm signals

Abstract When securing complex infrastructures or large environments, constant surveillance of every area is not affordable. To cope with this issue, a common countermeasure is the usage of cheap but wide-ranged sensors, able to detect suspicious events that occur in large areas, supporting patrollers to improve the effectiveness of their strategies. However, such sensors are commonly affected by uncertainty. In the present paper, we focus on spatially uncertain alarm signals. That is, the alarm system is able to detect an attack but it is uncertain on the exact position where the attack is taking place. This is common when the area to be secured is wide, such as in border patrolling and fair site surveillance. We propose, to the best of our knowledge, the first Patrolling Security Game where a Defender is supported by a spatially uncertain alarm system, which non-deterministically generates signals once a target is under attack. We show that finding the optimal strategy is FNP -hard even in tree graphs and APX -hard in arbitrary graphs. We provide two (exponential time) exact algorithms and two (polynomial time) approximation algorithms. Finally, we show that, 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, which, unfortunately, affect every commercial alarm system. We evaluate our methods in simulation, assessing both quantitative and qualitative aspects.

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 (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.

Computing the Team–maxmin Equilibrium in Single–Team Single–Adversary Team Games

A team game is a non–cooperative normal–form game in which some teams of players play against others. Team members share a common goal but, due to some constraints, they cannot act jointly. A real–world example is the protection of environments or complex infrastructures by different security agencies: they all protect the area with valuable targets but they have to act individually since they cannot share their defending strategies (of course, they are aware of the presence of the other agents). Here, we focus on zero–sum team games with n players, where a team of n ́ 1 players plays against one single adversary. In these games, the most appropriate solution concept is the Team–maxmin equilibrium, i.e., the Nash equilibrium that ensures the team the highest payoff. We investigate the Team–maxmin equilibrium, characterizing the utility of the team and showing that it can be irrational. The problem of computing such equilibrium is NP–hard and cannot be approximated within a factor of 1 n . The exact solution can only be found by global optimization. We propose two approximation algorithms: the former is a modified version of an already existing algorithm, the latter is a novel anytime algorithm. We computationally investigate such algorithms, providing bounds on the utility for the team. We experimentally evaluate the algorithms analyzing their performance w.r.t. a global optimization approach and evaluate the loss due to the impossibility of correlating.