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Patrolling Games

Author

Listed:
  • Steve Alpern

    (Department of Mathematics and Management Science Group, Department of Management, London School of Economics and Political Science, London WC2A 2AE, United Kingdom)

  • Alec Morton

    (Management Science Group, Department of Management, London School of Economics and Political Science, London WC2A 2AE, United Kingdom)

  • Katerina Papadaki

    (Management Science Group, Department of Management, London School of Economics and Political Science, London WC2A 2AE, United Kingdom)

Abstract

A key operational problem for those charged with the security of vulnerable facilities (such as airports or art galleries) is the scheduling and deployment of patrols. Motivated by the problem of optimizing randomized, and thus unpredictable, patrols, we present a class of patrolling games. The facility to be patrolled can be thought of as a network or graph Q of interconnected nodes (e.g., rooms, terminals), and the Attacker can choose to attack any node of Q within a given time T . He requires m consecutive periods there, uninterrupted by the Patroller, to commit his nefarious act (and win). The Patroller can follow any path on the graph. Thus, the patrolling game is a win-lose game, where the Value is the probability that the Patroller successfully intercepts an attack, given best play on both sides. We determine analytically either the Value of the game, or bounds on the Value, for various classes of graphs, and we discuss possible extensions and generalizations.

Suggested Citation

  • Steve Alpern & Alec Morton & Katerina Papadaki, 2011. "Patrolling Games," Operations Research, INFORMS, vol. 59(5), pages 1246-1257, October.
    • Handle: RePEc:inm:oropre:v:59:y:2011:i:5:p:1246-1257
    DOI: 10.1287/opre.1110.0983
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    References listed on IDEAS

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    Cited by:

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    2. Lidbetter, Thomas, 2017. "On the approximation ratio of the Random Chinese Postman Tour for network search," European Journal of Operational Research, Elsevier, vol. 263(3), pages 782-788.

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