Deterring criminals with limited police resources is a difficult task because the location of the criminal changes over time. The size of the vast transportation network further increases the difficulty of such scenarios. To address this problem, we consider the concept of hierarchical graphs. At each time point, we create a copy of the entire transportation network to track the possible movements of both the attacker and the defender. We consider the Stackelberg game in a dynamic crime scenario where the attacker changes his location over time while the defender tries to deter the attacker from his escape path. Given a set of defender strategies, we apply Dijkstra's algorithm on the hierarchical network to determine the optimal attacker strategy, where the attacker aims to minimize and the defender aims to maximize the deterrence probability. We develop an approximation algorithm on the hierarchical network to find the near-optimal strategy for the defender. The effectiveness of the developed approach is compared with the adopted MILP approach. We compare the results in terms of computation time and solution quality. The quality of the results demonstrates the necessity of the developed approach as it effectively solves complex problems in a short time.
