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Coordinating resources in Stackelberg Security Games

Author

Listed:
  • Bucarey L., Víctor
  • Casorrán, Carlos
  • Labbé, Martine
  • Ordoñez, Fernando
  • Figueroa, Oscar

Abstract

In this work we formulate a Stackelberg Security Game that coordinates resources in a border patrol problem. In this security domain, resources from different precincts have to be paired to conduct patrols in the border due to logistic constraints. Given this structure, models that enumerate the pure defender strategies scale poorly. We describe the set of mixed strategies using a polynomial number of variables but exponentially many constraints that come from the matching polytope. We then include this description in a mixed integer formulation to compute the Strong Stackelberg Equilibrium efficiently with a branch and cut scheme. Since the optimal patrol solution is a probability distribution over the set of exponential size, we also introduce an efficient sampling method that can be used to deploy the security resources every shift. Our computational results evaluate the efficiency of the branch and cut scheme developed and the accuracy of the sampling method.

Suggested Citation

  • Bucarey L., Víctor & Casorrán, Carlos & Labbé, Martine & Ordoñez, Fernando & Figueroa, Oscar, 2021. "Coordinating resources in Stackelberg Security Games," European Journal of Operational Research, Elsevier, vol. 291(3), pages 846-861.
    • Handle: RePEc:eee:ejores:v:291:y:2021:i:3:p:846-861
    DOI: 10.1016/j.ejor.2019.11.002
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    Cited by:

    1. Wang, Jian & Cui, Lei, 2023. "Patrolling games with coordination between monitoring devices and patrols," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    2. Guzmán, Cristóbal & Riffo, Javiera & Telha, Claudio & Van Vyve, Mathieu, 2022. "A sequential Stackelberg game for dynamic inspection problems," European Journal of Operational Research, Elsevier, vol. 302(2), pages 727-739.

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