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

• Published in: European journal of operational research Vol. 273; no. 3; pp. 1065 - 1073
• Main Authors: Alpern, Steve, Lidbetter, Thomas, Papadaki, Katerina
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 16-03-2019
• Subjects: Game Theory; Networks; Search/Surveillance; Game Theory; Networks; Search/Surveillance
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2018.08.050

•Periodic patrolling games: Patroller versus attacker.•Attack duration two time periods.•For time horizon even, game is solved for arbitrary graphs.•Complete solution for line graph.•Results for multiple patrollers.
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.