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Patrolling games

Author

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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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    1. Gerald Brown & Matthew Carlyle & Javier Salmerón & Kevin Wood, 2006. "Defending Critical Infrastructure," Interfaces, INFORMS, vol. 36(6), pages 530-544, December.
    2. Avenhaus, Rudolf & Von Stengel, Bernhard & Zamir, Shmuel, 2002. "Inspection games," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 51, pages 1947-1987, Elsevier.
    3. Craig R. Fox & David Bardolet & Daniel Lieb, 2005. "Partition Dependence in Decision Analysis, Resource Allocation, and Consumer Choice," Springer Books, in: Rami Zwick & Amnon Rapoport (ed.), Experimental Business Research, chapter 0, pages 229-251, Springer.
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    Cited by:

    1. 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.
    2. Laan, Corine M. & van der Mijden, Tom & Barros, Ana Isabel & Boucherie, Richard J. & Monsuur, Herman, 2017. "An interdiction game on a queueing network with multiple intruders," European Journal of Operational Research, Elsevier, vol. 260(3), pages 1069-1080.
    3. Ríos Insua, David & Cano, Javier & Pellot, Michael & Ortega, Ricardo, 2016. "Multithreat multisite protection: A security case study," European Journal of Operational Research, Elsevier, vol. 252(3), pages 888-899.
    4. Oléron Evans, Thomas P. & Bishop, Steven R., 2013. "Static search games played over graphs and general metric spaces," European Journal of Operational Research, Elsevier, vol. 231(3), pages 667-689.
    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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