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Patrolling games

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  • Alpern, Steven
  • Morton, Alec
  • Papadaki, Katerina

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. Subject classifications: games; noncooperative; military, search/surveillance; decision analysis; risk; networks/graphs. Area of review: Military and Homeland Security. History: Received November 2009; revisions received March 2010, September 2010; accepted November 2010

Suggested Citation

  • Alpern, Steven & Morton, Alec & Papadaki, Katerina, 2011. "Patrolling games," LSE Research Online Documents on Economics 32210, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:32210
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    File URL: http://eprints.lse.ac.uk/32210/
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    References listed on IDEAS

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    Cited by:

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    5. 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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    More about this item

    Keywords

    ISI; games; noncooperative; military; search/surveillance; decision analysis; risk; networks/graphs;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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