Optimizing periodic patrols against short attacks on the line and other networks

On a given network, a Patroller and Attacker play the following win-lose game: The Patroller adopts a periodic walk on the network while the Attacker chooses a node and two consecutive periods (to attack there). The Patroller wins if he successfully intercepts the attack, that is, if he occupies the attacked node in one of the two periods of the attack. We solve this game in mixed strategies for line graphs, the first class of graphs to be solved for the periodic patrolling game. We also solve the game for arbitrary graphs when the period is even

Volume 105 Issue 14

https://dc.swosu.edu/the_southwestern/1076/thumbnail.jp

Patrolling a border

Patrolling games were recently introduced by Alpern, Morton and Papadaki to model the problem of protecting the nodes of a network from an attack. Time is discrete and in each time unit the Patroller can stay at the same node or move to an adjacent node. The Attacker chooses when to attack and which node to attack, and needs m consecutive time units to carry it out. The Attacker wins if the Patroller does not visit the chosen node while it is being attacked; otherwise the Patroller wins. This paper studies the patrolling game where the network is a line graph of n nodes, which models the problem of guarding a channel or protecting a border from infiltration. We solve the patrolling game for any values of m and n, providing an optimal Patroller strategy, an optimal Attacker strategy and the value of the game (optimal probability that the attack is intercepted)

Adversarial patrolling in a uniform

Patrolling games were introduced by Alpern, Morton, and Papadaki in 2011 to model the adversarial problem where a mobile Patroller can thwart an attack at some location only by visiting it during the attack period, which has a prescribed integer duration. In this note, we modify the problem by allowing the Attacker to go to his planned attack location early and observe the presence or the absence there of the Patroller (who wears a uniform). To avoid being too predictable, the Patroller may sometimes remain at her base when she could have been visiting a possible attack location. The Attacker can then choose to delay attacking for some number of periods after the Patroller leaves his planned attack location. As shown here, this extra information for the Attacker can reduce thwarted attacks by as much as a factor of four in some cases. Our main finding is that the attack should begin in the second period the Patroller is away and the Patroller should never visit the same location (other than her base) in consecutive periods

Game theoretic models of networks security

Decision making in the context of crime execution and crime prevention can be successfully investigated with the implementation of game-theoretic tools. Evolutionary and mean-field game theory allow for the consideration of a large number of interacting players organized in social and behavioural structures, which typically characterize this context. Alternatively, `traditional' game-theoretic approaches can be applied for studying the security of an arbitrary network on a two player non-cooperative game. Theoretically underpinned by these instruments, in this thesis we formulate and analyse game-theoretic models of inspection, corruption, counter- terrorism, patrolling, and similarly interpreted paradigms. Our analysis suggests optimal strategies for the involved players, and illustrates the long term behaviour of the introduced systems. Our contribution is towards the explicit formulation and the thorough analysis of real life scenaria involving the security in network structures

Viet Nam Generation, Volume 7, Number 1-2

Edited by Dan Duffy and Kali Tal. Contributing editors: Renny Christopher. David DeRose, Alan Farrell. Cynthia Fuchs, William M. King. Bill Shields, Tony Williams, and David Willson