Network Design and Imperfect Defense

Abstract

We address the problem of how to optimally design an infrastructure network that may be subject to intelligent attacks by considering a Designer-Adversary game of optimal network design for the cases of imperfect node- and link defense. In this two-stage game, first the Designer defends network connectivity by forming costly links and additionally protecting nodes (links). Then, the Adversary attacks a fixed number of nodes (links), aiming to disconnect the network. In contrast to the existing literature, defense is imperfect in the sense that defended nodes (links) can still be destroyed with some fixed probability.

We completely characterize the solution of the game for attack budgets of one and two nodes or links, while for larger budget we present a partial characterization of the solution. To do so, we determine the minimum number of links necessary to construct a network with any degree of connectivity and any given number of essential nodes.

Keywords: Network Design, Network Defense, Designer-Adversary Games, Node Destruction, Link Destruction

JEL Classification: C69, C72, D85