Design of Network Topology in an Adversarial Environment

We study the strategic interaction between a network manager whose goal is to choose (as communication infrastructure) a spanning tree of a network given as an undirected graph, and an attacker who is capable of attacking a link in the network. We model their interaction as a zero-sum game and discuss a particular set of Nash equilibria. More specifically, we show that there always exists a Nash equilibrium under which the attacker targets a critical set of links. A set of links is called critical if it has maximum vulnerability, and the vulnerability of a set of links is defined as the minimum fraction of links the set has in common with a spanning tree. Using simple examples, we discuss the importance of critical subsets in the design of networks that are aimed to be robust against attackers. Finally, an algorithm is provided, to compute a critical subset of a given graph.