The Uniformed Patroller Game

TL;DR

This paper analyzes a network patrolling game where the Patroller's visibility affects the Attacker's strategy, providing solutions for various network structures under Markovian strategies.

Contribution

It introduces a new variant of the network patrolling game accounting for Patroller identification, and solves it for multiple network types with Markovian strategies.

Findings

Optimal strategies depend on network topology.

Identification of the impact of Patroller visibility on attack success.

Solutions provided for star, line, circle, and mixed networks.

Abstract

In the recently introduced network patrolling game, an Attacker carries out an attack on a node of her choice, for a given number m of consecutive periods. The parameter m indicates the difficulty of the attack at a given node. To thwart such an attack, the Patroller adopts a walk on the network, hoping to be at the attacked node during one of the m periods. If this occurs, the attack is interrupted and the Patroller wins; otherwise the Attacker wins. In the original setting, the Attacker has no knowledge of the Patroller's location at any time. Here, to model the important alternative where the Patroller can be identified when he is at the Attacker's node (e.g. the Patroller wears a uniform), we allow the Attacker to initiate her attack after waiting for a chosen number d of consecutive periods in which the Patroller has been away. We solve this version of the game for various networks: star, line, circle and a mixture. We restrict the Patroller to Markovian strategies, which cover the whole network.