Abstract
We present a decision support system to help plan preventive border patrols. The system represents the interaction between defenders and intruders as a Stackelberg security game (SSG) where the defender pools local resources to conduct joint preventive border patrols. We introduce a new SSG that constructs defender strategies that pair adjacent precincts to pool resources that are used to patrol a location within one of the two precincts. We introduce an efficient formulation of this problem and an efficient sampling method to construct an implementable defender strategy.
The system automatically constructs the Stackelberg game from geographically located past crime data, topology and cross border information. We use clustering of past crime data and logit probability distribution to assign risk to patrol areas. Our results on a simplified real-world inspired border patrol instance show the computational efficiency of the model proposed, its robustness with respect to parameters used in automatically constructing the instance, and the quality of the sampled solution obtained.
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References
Council of the EU: European border and coast guard: final approval (2016). http://www.consilium.europa.eu/en/press/press-releases/2016/09/14-european-border-coast-guard/. Accessed Feb 2017
Department of Homeland Security: Border security (2017). https://www.dhs.gov/border-security. Accessed Feb 2017
von Stackelberg, H.: Principios de teoria economica. Oxford University Press, New York (1952)
Bracken, J., McGill, J.T.: Mathematical programs with optimization problems in the constraints. Oper. Res. 21(1), 37–44 (1973)
Jain, M., Tsai, J., Pita, J., Kiekintveld, C., Rathi, S., Tambe, M., Ordóñez, F.: Software assistants for randomized patrol planning for the lax airport police and the federal air marshal service. Interfaces 40(4), 267–290 (2010)
Shieh, E., An, B., Yang, R., Tambe, M., Baldwin, C., DiRenzo, J., Maule, B., Meyer, G.: Protect: a deployed game theoretic system to protect the ports of the United States. In: Richland, S. (ed.) Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2012, Richland, SC, vol. 1, pp. 13–20. International Foundation for Autonomous Agents and Multiagent Systems (2012)
Yin, Z., Jiang, A.X., Tambe, M., Kiekintveld, C., Leyton-Brown, K., Sandholm, T., Sullivan, J.P.: Trusts: scheduling randomized patrols for fare inspection in transit systems using game theory. AI Mag. 33(4), 59–72 (2012)
Yang, R., Ford, B., Tambe, M., Lemieux, A.: Adaptive resource allocation for wildlife protection against illegal poachers. In: International Conference on Autonomous Agents and Multiagent Systems (AAMAS) (2014)
Kiekintveld, C., Jain, M., Tsai, J., Pita, J., Ordóñez, F., Tambe, M.: Computing optimal randomized resource allocations for massive security games. In: Proceedings of The 8th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2009, Richland, SC, vol. 1, pp. 689–696. International Foundation for Autonomous Agents and Multiagent Systems (2009)
Paruchuri, P., Pearce, J.P., Marecki, J., Tambe, M., Ordóñez, F., Kraus, S.: Playing games for security: an efficient exact algorithm for solving Bayesian Stackelberg games. In: Proceedings of the 7th International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS 2008, Richland, SC, vol. 2, pp. 895–902. International Foundation for Autonomous Agents and Multiagent Systems (2008)
Leitman, G.: On generalized Stackelberg strategies. J. Optim. Theor. Appl. 26(4), 637–643 (1978)
Edmonds, J.: Maximum matching and a polyhedron with 0, l-vertices. J. Res. Nat. Bur. Stand. B 69(1965), 125–130 (1965)
Farkas, J.: Theorie der einfachen ungleichungen. Journal für die reine und angewandte Mathematik 124, 1–27 (1902)
Schrijver, A.: Combinatorial Optimization - Polyhedra and Efficiency. Springer, Heidelberg (2003)
QGIS: QGIS Geographic Information System. Open Source Geospatial Foundation (2009)
Comisión Económica para América Latina y el Caribe: Costo económico de los delitos, niveles de vigilancia y políticas de seguridad ciudadana en las comunas del gran santiago (2000). http://www.cepal.org/es/publicaciones/7258-costo-economico-de-los-delitos-niveles-de-vigilancia-y-politicas-de-seguridad
Aduanas de Chile: Qué tributos deben pagar las importaciones? (2016). https://www.aduana.cl/importaciones-de-productos/aduana/2007-02-28/161116.html
Ministerio del Trabajo y Previsión Social: Reajusta monto del ingreso mínimo mensual, de la asignación familiar y maternal del subsidio familiar, para los periodos que indica (2016). http://www.leychile.cl/Navegar?idLey=20763
Kullback, S., Leibler, R.A.: On information and sufficiency. Ann. Math. Stat. 22(1), 79–86 (1951)
Acknowledgements
Casorrán wishes to acknowledge the FNRS for funding his PhD research through a FRIA grant. This work is also partially supported by the Interuniversity Attraction Poles Programme P7/36 “COMEX” initiated by the Belgian Science Policy Office. Ordóñez acknowledges the support by CONICYT through Fondecyt grant 1140807 and the Complex Engineering Systems Institute, ISCI (CONICYT: FB0816).
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Bucarey, V., Casorrán, C., Figueroa, Ó., Rosas, K., Navarrete, H., Ordóñez, F. (2017). Building Real Stackelberg Security Games for Border Patrols. In: Rass, S., An, B., Kiekintveld, C., Fang, F., Schauer, S. (eds) Decision and Game Theory for Security. GameSec 2017. Lecture Notes in Computer Science(), vol 10575. Springer, Cham. https://doi.org/10.1007/978-3-319-68711-7_11
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