Linear Loss Function for the Network Blocking Game: An Efficient Model for Measuring Network Robustness and Link Criticality

In order to design robust networks, first, one has to be able to measure robustness of network topologies. In [1], a game-theoretic model, the network blocking game, was proposed for this purpose, where a network operator and an attacker interact in a zero-sum game played on a network topology, and the value of the equilibrium payoff in this game is interpreted as a measure of robustness of that topology. The payoff for a given pair of pure strategies is based on a loss-in-value function. Besides measuring the robustness of network topologies, the model can be also used to identify critical edges that are likely to be attacked. Unfortunately, previously proposed loss-in-value functions are either too simplistic or lead to a game whose equilibrium is not known to be computable in polynomial time. In this paper, we propose a new, linear loss-in-value function, which is meaningful and leads to a game whose equilibrium is efficiently computable. Furthermore, we show that the resulting game-theoretic robustness metric is related to the Cheeger constant of the topology graph, which is a well-known metric in graph theory.