Abstract
This paper presents a game theoretic model that analyzes resource allocation strategies against an adaptive adversary to secure cargo container transportation. The defender allocates security resources that could interdict an unauthorized weapon insertion inside a container. The attacker observes the defender’s security strategy and chooses a site to insert the weapon. The attacker’s goal is to maximize the probability that the weapon reaches its target. The basic model includes a single container route. The results in the basic model suggest that in equilibrium the defender should maintain an equal level of physical security at each site on the cargo container’s route. Furthermore, the equilibrium levels of resources to interdict the weapon overseas increase as a function of the attacker’s capability to detonate the weapon remotely at a domestic seaport. Investment in domestic seaport security is highly sensitive to the attacker’s remote detonation capability as well. The general model that includes multiple container routes suggests that there is a trade-off between the security of foreign seaports and the physical security of sites including container transfer facilities, container yards, warehouses and truck rest areas. The defender has the flexibility to shift resources between non-intrusive inspections at foreign seaports and physical security of other sites on the container route. The equilibrium is also sensitive to the cost effectiveness of security investments.
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References
Allison, G. (2004). Nuclear terrorism. New York: Times Books.
Allison, G. (2006). The will to prevent. Harvard International Review, 28(3), 50–55.
Bakır, N. O. (2008). A decision tree model for evaluating countermeasures to secure cargo at United States southwestern ports of entry. Decision Analysis, 5(4), 230–248.
Bakshi, N., Flynn, S. E., & Gans, N. (2009). Estimating the operational impact of container inspections at international ports (Working Paper No. 2009-05-01). The Wharton School Risk Management and Decision Processes Center.
Bier, V. M., Oliveros, S., & Samuelson, L. (2007). Choosing what to protect: Strategic defensive allocation against an unknown attacker. Journal of Public Economic Theory, 9(4), 563–587.
Bier, V. M., Haphuriwat, N., Menoyo, J., Zimmerman, R., & Culpen, A. M. (2008). Optimal resource allocation for defense of targets based on differing measures of attractiveness. Risk Analysis, 28(3), 763–770.
Boros, E., Fedzhora, L., Kantor, P. B., Saeger, K., & Stroud, P. (2006). Large scale LP model for finding optimal container inspection strategies (Rutcor Research Report No. RRR-26-2006).
Bunn, M., & Wier, A. (2006). Terrorist nuclear weapon construction: How difficult? The Annals of the American Academy of Political and Social Science, 607(1), 133–149.
Cohen, S. S. (2006). Boom boxes: Containers and terrorism. In J.D. Haveman & H.J. Shatz (Eds.), Protecting the nation’s seaports: Balancing security and cost (pp. 91–128).
Cooper, M. H. (2004). Nuclear proliferation and terrorism. CQ Researcher, 14(13), 297–320.
DHS (2005). National planning scenarios: Executive summaries. http://cees.tamiu.edu/covertheborder/TOOLS/NationalPlanningSen.pdf.
Elsayed, E. A., Young, C. M., Xie, M., Zhang, H., & Zhu, Y. (2007). Port-of-entry inspection: Sensor deployment policy optimization (Rutgers IE Working Paper 07-012).
Ferguson, C. D. (2006). Preventing catastrophic nuclear terrorism. Council on Foreign Relations Special Report, Washington, DC.
GAO (2005a). Cargo security: Partnership program grants importers reduced scrutiny with limited assurance of improved security. U.S. Government Accountability Office, GAO-05-404, Washington, DC.
GAO (2005b). Homeland security: Key cargo security programs can be improved. U.S. Government Accountability Office, GAO-05-466T, Washington, DC.
GAO (2008a). Supply chain security: Examinations of high-risk cargo at foreign seaports have increased, but improved data collection and performance measures are needed. U.S. Government Accountability Office, GAO-08-187, Washington, DC.
GAO (2008b). U.S. customs and border protection has enhanced its partnership with import trade sectors, but challenges remain in verifying security practices. U.S. Government Accountability Office, GAO-08-240, Washington, DC.
Golany, B., Kaplan, E. H., Marmur, A., & Rothblum, U. G. (2009). Nature plays with dice—terrorists do not: Allocating resources to counter strategic versus probabilistic risks. European Journal of Operational Research, 192(1), 198–208.
Hoffman, B. (2006). The use of the Internet by Islamic extremists. RAND Testimony, Santa Monica, CA.
IAEA (2006). Illicit trafficking and other unauthorized activities involving nuclear and radioactive materials. IAEA 2005 Fact Sheet.
Kardeş, E. (2007). Discounted robust stochastic games with applications to homeland security and flow control. Ph.D. Dissertation, University of Southern California.
Langewiesche, W. (2007). The atomic bazaar. New York: Farrar, Straus and Giroux.
Maerli, B. M., Schaper, A., & Barnaby, F. (2003). The characteristics of nuclear terrorist weapons. American Behavioral Scientist, 46(6), 727–744.
Major, J. A. (2002). Advanced techniques for modeling terrorism risk. Journal of Risk Finance, 4(1), 15–24.
Martin, B. (2007). Nuclear power and antiterrorism: Obscuring the policy contradictions. Prometheus, 25(1), 19–29.
Paruchuri, P., Tambe, M., Ordóñez, F., & Kraus, S. (2006a). Increasing security through communication and policy randomization in multiagent systems. In Proceedings of the AAMAS-2006 conference, Hakodate, Japan.
Paruchuri, P., Tambe, M., Ordóñez, F., & Kraus, S. (2006b). Security in multiagent systems by policy randomization. In Proceedings of the AAMAS-2006 conference, Hakodate, Japan.
Paruchuri, P., Pearce, J., Tambe, M., Ordóñez, F., & Kraus, S. (2007). An efficient heuristic approach for security against multiple adversaries. In Proceedings of the AAMAS-2007 Conference, Honolulu, HI.
Paruchuri, P., Pearce, J., Marecki, J., Tambe, M., Ordóñez, F., & Kraus, S. (2008). Playing games for security: An efficient exact algorithm for solving Bayesian Stackelberg games. In Proceedings of the AAMAS-2008 conference, Estoril, Portugal.
Pita, J., Jain, M., Marecki, J., Ordóñez, F., Portway, C., Tambe, M., Western, C., Paruchuri, P., & Kraus, S. (2008). Deployed ARMOR protection: The application of a game theoretic model for security at the Los Angeles international airport. In Proceedings of the AAMAS-2008 conference, Estoril, Portugal.
Powell, R. (2007). Defending against terrorist attacks with limited resources. The American Political Science Review, 101(3), 527–541.
Wein, L. M., Wilkins, A. H., Baveja, M., & Flynn, S. E. (2006). Preventing the importation of illicit nuclear materials in shipping containers. Risk Analysis, 26(5), 1377–1393.
Zhuang, J., & Bier, V. M. (2007). Balancing terrorism and natural disasters—Defensive strategy with endogenous attacker effort. Operations Research, 55(5), 976–991.
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Bakır, N.O. A Stackelberg game model for resource allocation in cargo container security. Ann Oper Res 187, 5–22 (2011). https://doi.org/10.1007/s10479-010-0793-z
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DOI: https://doi.org/10.1007/s10479-010-0793-z