Network sensing for security against link disruption attacks

We consider the problem of detecting security failures caused by a resource-constrained attacker using randomized sensing strategies. We propose a game-theoretic model in which the objective of the attacker (resp. defender) is to maximize the number of undetected attacks (resp. detections) on the network. Our game is strategically equivalent to a zero-sum game. Thus, the Nash Equilibria (NE) solution can be found by solving two linear programming (LP) problems. Still, characterization of equilibrium strategies is not tractable for large-scale networks. We assume that the defender's (resp. attacker's) detection (resp. attack) budget is limited relative to the size of the network. Under this assumption, we provide structural results on the equilibrium payoffs based on the players' resources and the size of the minimum set covers. We show that an equilibrium strategy of the defender is to choose a randomized sensing strategy that spans a minimum set cover. This result significantly improves the tractability of NE computation, and provides some practical insights on network sensing in adversarial environments.