  We consider an attacker-operator game for monitoring a large-scale network
that is comprised on components that differ in their criticality levels. In
this zero-sum game, the operator seeks to position a limited number of sensors
to monitor the network against an attacker who strategically targets a network
component. The operator (resp. attacker) seeks to minimize (resp. maximize) the
network loss. To study the properties of mixed-strategy Nash Equilibria of this
game, we first study two simple instances: (i) When component sets monitored by
individual sensor locations are mutually disjoint; (ii) When only a single
sensor is positioned, but with possibly overlapping monitoring component sets.
Our analysis reveals new insights on how criticality levels impact the players
equilibrium strategies. Next, we extend a previously known approach to obtain
an approximate Nash equilibrium for the general case of the game. This approach
uses solutions to minimum set cover and maximum set packing problems to
construct an approximate Nash equilibrium. Finally, we implement a column
generation procedure to improve this solution and numerically evaluate the
performance of our approach.
