System survivability in the context of interdiction networks

•We introduce the concept of network survivability under attack.•We treat the problem as a game and investigate Nash equilibrium.•We develop results to estimate two types of network survivability•We compare both types of survivability against network reliability.•We treat the large scale of networks as well as a number of extensions. We define the concept of network survivability in the context of defense/attack strategies. We assume that a network is threatened by attackers. The attacker is referred to as a leader that targets selected links. Typically, the overall attack is considered as successful if the network is disabled. The follower is interested in preserving the functionality of the network and may restrict the network operation to limited paths. His/her problem is to determine which optimal set of paths to operate with the highest probability to survive an attack; while the leader seeks to determine which links to target to maximize the chance of a successful attack. In case of absence of knowledge, we distinguish two types of network survivability related to the follower and to the leader of the network, respectively. The latter has to do with partitioning the network. Both types are compared against each other as well as against network reliability. We derive a number of results both under the cases of full and absence of knowledge. We model the problem as a game and investigate the best strategy of each player as well as the cases of occurrence of equilibrium in a variety of settings.