Survivable Network Design under Various Interdiction Scenarios

We examine the problem of building or fortifying a network to defend against enemy attack scenarios. In particular, we examine the case in which an enemy can destroy all or part of the arcs that we construct on the network, subject to some interdiction budget. This problem takes the form of a three-level, two-player game, in which we act first to construct our network and simultaneously transmit an initial set of flows through the network. The enemy acts next to destroy a set of constructed arcs in our network, and we act last to transmit a final set of flows in the network. Most studies of this nature assume that the enemy will act optimally; however, in real-world scenarios one cannot assume rationality on the part of the enemy. Hence, we prescribe network design principals for three different profiles of enemy action: an enemy destroying arcs based on capacities, based on initial flows, or acting optimally to minimize our maximum revenues obtained from transmitting flows.