Strategic network interdiction

We develop a strategic model of network interdiction. Given a network, an agency faces an adversary. The adversary chooses how to carry bads through the network from a base to a target. By carrying bads, the adversary can damage the target. Simultaneously, the agency chooses which arcs to block in the network. By blocking arcs, the agency can decrease the amount of bads carried to the target. However, the blockage of arcs disrupts the operation of the network. The adversary gains from the target damage and the network disruption while the agency loses from them. The adversary incurs the expense of carrying bads. We find Nash equilibria of this model. When the marginal loss of the target is no greater than the marginal expense of carrying bads, there are pure strategy Nash equilibria in which the adversary carries no bads from the base to the target and the agency blocks no arcs. When the marginal loss of the target is greater than the marginal expense of carrying bads, there are mixed strategy Nash equilibria in which the adversary carries certain amounts of bads with positive probability and the agency blocks no arcs with positive probability. We then calculate the equilibrium probabilities of the adversary damaging the target. These equilibrium probabilities turn out to be negative power functions of the marginal target loss.