Stochastic dynamic network interdiction games

Network interdiction problems consist of games between an attacker and an intelligent network, where the attacker seeks to degrade network operations while the network adapts its operations to counteract the effects of the attacker. This problem has received significant attention in recent years due to its relevance to military problems and network security. When the attacker´s actions achieve uncertain effects, the resulting problems become stochastic network interdiction problems, and allow the players to adapt to new information collected during the game. In this paper, we study stochastic network interdiction games where the attacker has one or two stages to attack the network, and can collect information on the outcomes of previous attacks. For the single stage problem, we develop a new solution algorithm, based on parsimonious integration of branch and bound techniques with increasingly accurate lower bounds, that obtains solutions significantly faster than previous approaches in the literature. We extend the single stage formulation to a two stage formulation, and develop a new set of performance bounds for this problem. We integrate these bounds into a modified branch and bound procedure that extends the single stage approach to two stages. The efficacy of the new algorithms is shown using simulated experiments with networks studied in previous papers.