Continuous Patrolling Games

Steve Alpern (), Thuy Bui (), Thomas Lidbetter () and Katerina Papadaki ()
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Steve Alpern: Warwick Business School, University of Warwick, Coventry CV4 7AL, United Kingdom
Thuy Bui: Rutgers Business School, Newark, New Jersey 07102
Thomas Lidbetter: Rutgers Business School, Newark, New Jersey 07102; Department of Engineering Systems and Environment, University of Virginia, Charlottesville, Virginia 22904
Katerina Papadaki: Department of Mathematics, London School of Economics, London WC2A 2AE, United Kingdom

Operations Research, 2022, vol. 70, issue 6, 3076-3089

Abstract: We study a patrolling game played on a network Q , considered as a metric space. The Attacker chooses a point of Q (not necessarily a node) to attack during a chosen time interval of fixed duration. The Patroller chooses a unit speed path on Q and intercepts the attack (and wins) if she visits the attacked point during the attack-time interval. This zero-sum game models the problem of protecting roads or pipelines from an adversarial attack. The payoff to the maximizing Patroller is the probability that the attack is intercepted. Our results include the following: (i) a solution to the game for any network Q , as long as the time required to carry out the attack is sufficiently short; (ii) a solution to the game for all tree networks that satisfy a certain condition on their extremities; and (iii) a solution to the game for any attack duration for stars with one long arc and the remaining arcs equal in length. We present a conjecture on the solution of the game for arbitrary trees and establish it in certain cases.

Keywords: Military and Homeland Security; patrolling; zero-sum games; networks (search for similar items in EconPapers)
Date: 2022
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