  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.
