Approximation Approaches for Solving Security Games with Surveillance Cost: A Preliminary Study

Security game models have been deployed to allocate limited security resources for critical infrastructure protection. Much work on this topic assumes that attackers have perfect knowledge of the defender’s randomized strategy. However, this assumption is not realistic, considering surveillance cost, since attackers may only have partial knowledge of the defender’s strategies, and may dynamically decide whether to attack or conduct more surveillance. Recently, a model called OPTS (OPtimal sTopping Security games) considered surveillance cost and formulated the attacker’s optimal decision making problem as a finite state space MDP (Markov Decision Process). However, the known exact algorithms for this MDP cannot scale up. In this paper, we extend several approximation approaches based on the MCTS (MonteCarlo Tree Search) method and RTDP (Real-Time Dynamic Programming) to MDPs of the OPTS model. We also propose an iterative deepening based approximation algorithm. Experimental results show that these approaches can solve much larger security games with surveillance cost.