Optimal defensive resource allocation for a centrality-based security game on multi-hop networks

We present a new analysis of multi-hop network security in the form of a zero-sum game played between an attacker who tries to disrupt a network by disabling one or more nodes, and the nodes of the network who must allocate limited resources in defense of the network. The payoffs in the zero-sum game can be one of several performance metrics that correspond to node centrality measures. In the case of single-node attacks, we use a monotonicity property of the mixed attack strategies to construct a simple and very fast algorithm to compute saddle-point equilibrium strategies for both single-node and multiple-node defense. For simultaneous multiple-node attacks on large networks, the computational complexity becomes quite high, so we present a method to approximate the equilibrium strategies based on a sequential simplification, which performs well in simulations.