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Patrolling a Border

Author

Listed:
  • Katerina Papadaki

    (Department of Mathematics, London School of Economics, London WC2A 2AE, United Kingdom)

  • Steve Alpern

    (Warwick Business School, University of Warwick, Coventry CV4 7AL, United Kingdom)

  • Thomas Lidbetter

    (Rutgers Business School, Department of Management Science and Information Systems, Newark, New Jersey 07102)

  • Alec Morton

    (Department of Management Science, University of Strathclyde, Glasgow G1 1XQ, United Kingdom)

Abstract

Patrolling games were recently introduced 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).

Suggested Citation

  • Katerina Papadaki & Steve Alpern & Thomas Lidbetter & Alec Morton, 2016. "Patrolling a Border," Operations Research, INFORMS, vol. 64(6), pages 1256-1269, December.
    • Handle: RePEc:inm:oropre:v:64:y:2016:i:6:p:1256-1269
    DOI: 10.1287/opre.2016.1511
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    References listed on IDEAS

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    1. Vic Baston & Kensaku Kikuta, 2009. "Technical Note---An Ambush Game with a Fat Infiltrator," Operations Research, INFORMS, vol. 57(2), pages 514-519, April.
    2. V. J. Baston & F. A. Bostock, 1987. "A continuous game of ambush," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(5), pages 645-654, October.
    3. Kyle Y. Lin & Michael P. Atkinson & Timothy H. Chung & Kevin D. Glazebrook, 2013. "A Graph Patrol Problem with Random Attack Times," Operations Research, INFORMS, vol. 61(3), pages 694-710, June.
    4. Vic Baston & Kensaku Kikuta, 2004. "An Ambush Game with an Unknown Number of Infiltrators," Operations Research, INFORMS, vol. 52(4), pages 597-605, August.
    5. Roberto Szechtman & Moshe Kress & Kyle Lin & Dolev Cfir, 2008. "Models of sensor operations for border surveillance," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(1), pages 27-41, February.
    6. Kyle Y. Lin & Michael P. Atkinson & Kevin D. Glazebrook, 2014. "Optimal patrol to uncover threats in time when detection is imperfect," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(8), pages 557-576, December.
    7. Baykal-Gürsoy, Melike & Duan, Zhe & Poor, H. Vincent & Garnaev, Andrey, 2014. "Infrastructure security games," European Journal of Operational Research, Elsevier, vol. 239(2), pages 469-478.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. G. Liuzzi & M. Locatelli & V. Piccialli & S. Rass, 2021. "Computing mixed strategies equilibria in presence of switching costs by the solution of nonconvex QP problems," Computational Optimization and Applications, Springer, vol. 79(3), pages 561-599, July.
    2. Baston, Vic & Kikuta, Kensaku, 2019. "A search problem on a bipartite network," European Journal of Operational Research, Elsevier, vol. 277(1), pages 227-237.
    3. Alpern, Steve & Lidbetter, Thomas & Papadaki, Katerina, 2019. "Optimizing periodic patrols against short attacks on the line and other networks," European Journal of Operational Research, Elsevier, vol. 273(3), pages 1065-1073.
    4. Hunt, Kyle & Zhuang, Jun, 2024. "A review of attacker-defender games: Current state and paths forward," European Journal of Operational Research, Elsevier, vol. 313(2), pages 401-417.
    5. Darlington, Matthew & Glazebrook, Kevin D. & Leslie, David S. & Shone, Rob & Szechtman, Roberto, 2023. "A stochastic game framework for patrolling a border," European Journal of Operational Research, Elsevier, vol. 311(3), pages 1146-1158.
    6. Garrec, Tristan, 2019. "Continuous patrolling and hiding games," European Journal of Operational Research, Elsevier, vol. 277(1), pages 42-51.
    7. Wang, Jian & Cui, Lei, 2023. "Patrolling games with coordination between monitoring devices and patrols," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    8. Zhang, Laobing & Reniers, Genserik & Chen, Bin & Qiu, Xiaogang, 2019. "CCP game: A game theoretical model for improving the scheduling of chemical cluster patrolling," Reliability Engineering and System Safety, Elsevier, vol. 191(C).

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    Keywords

    search and surveillance; patrolling;

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