# A Network Monitoring Game with Heterogeneous Component Criticality Levels

## TL;DR

This paper models a strategic network monitoring game with components of varying criticality, analyzing equilibrium strategies and proposing an approximation method using set cover and packing solutions, validated through numerical experiments.

## Contribution

It introduces a novel game-theoretic model for heterogeneous network components and develops an approximation approach for equilibrium strategies using combinatorial optimization techniques.

## Key findings

- Criticality levels significantly influence equilibrium strategies.
- The proposed approximation method effectively estimates Nash equilibria.
- Numerical results demonstrate the approach's performance improvements.

## Abstract

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.