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Alpern, Steve, Bui, Thuy, Lidbetter, Thomas and Papadaki, Katerina (2022) Continuous patrolling games. Operations Research . doi:10.1287/opre.2022.2346 ISSN 0030-364X. (In Press)
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Official URL: https://doi.org/10.1287/opre.2022.2346
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 sufficintly 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.
| Item Type: | Journal Article | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QR Microbiology | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Journal or Publication Title: | Operations Research | ||||||||
| Publisher: | Institute for Operations Research and the Management Sciences (I N F O R M S) | ||||||||
| ISSN: | 0030-364X | ||||||||
| Official Date: | 2022 | ||||||||
| Dates: |
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| DOI: | 10.1287/opre.2022.2346 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | In Press | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Copyright Holders: | Copyright © 2022, INFORMS | ||||||||
| Date of first compliant deposit: | 14 November 2022 | ||||||||
| Date of first compliant Open Access: | 14 November 2022 | ||||||||
| Related URLs: |
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