A double oracle algorithm for allocating resources on nodes in graph-based security games

In the graph-based security game, the defender allocates security resources strategically to protect targets against the adversary. In this paper, firstly, we come up with a new double oracle algorithm for scheduling resources optimally on nodes in graph-based security games. The police scattered on the street can only detect those terrorists on that street, while the police at the intersection place can detect all the terriorists on all the streets crisscrossing the intersection. Secondly, in real world situation, even the police meets the criminals at the same place, criminals still could escape. To match the real world situation, we define a parameter called detection probability, representing the chance the attacker is caught when they are checked by the defenders. Thirdly, we design a double oracle algorithm to find the equilibrium. But the computational complexity of best response oracles are extremely high. We design greedy algorithms and combine them with best response oracles to improve the algorithm efficiency without loss of correctness.