A Centrality-Based Security Game for Multihop Networks

We formulate a network security problem as a zero-sum game 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 to defend the network. The utility of the zero-sum game can be one of several network performance metrics that correspond to node centrality measures. We first present a fast centralized algorithm that uses a monotone property of the utility function to compute saddle-point equilibrium strategies for the case of single-node attacks and singleor multiple-node defense. We then extend the approach to the distributed setting by computing the necessary quantities using a finite-time distributed averaging algorithm. For simultaneous attacks to multiple nodes, the computational complexity grows quickly, so we propose a method to approximate the saddle-point equilibrium strategies based on sequential simplification, which performs well in simulations.