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Nature plays with dice - terrorists do not: Allocating resources to counter strategic versus probabilistic risks


  • Golany, Boaz
  • Kaplan, Edward H.
  • Marmur, Abraham
  • Rothblum, Uriel G.


Probabilistic uncertainty is caused by "chance", whereas strategic uncertainty is caused by an adverse interested party. Using linear impact functions, the problems of allocating a limited resource to defend sites that face either probabilistic risk or strategic risk are formulated as optimization problems that are solved explicitly. The resulting optimal policies differ - under probabilistic risk, the optimal policy is to focus the investment of resources on priority sites where they yield the highest impact, while under strategic risk, the best policy is to spread the resources so as to decrease the potential damage level of the most vulnerable site(s). Neither solution coincides with the commonly practiced proportionality allocation scheme.

Suggested Citation

  • Golany, Boaz & Kaplan, Edward H. & Marmur, Abraham & Rothblum, Uriel G., 2009. "Nature plays with dice - terrorists do not: Allocating resources to counter strategic versus probabilistic risks," European Journal of Operational Research, Elsevier, vol. 192(1), pages 198-208, January.
  • Handle: RePEc:eee:ejores:v:192:y:2009:i:1:p:198-208

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    References listed on IDEAS

    1. Coughlin, Peter J, 1992. "Pure Strategy Equilibria in a Class of Systems Defense Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(3), pages 195-210.
    2. Kaplan, Edward H. & Pollack, Harold, 1998. "Allocating HIV Prevention Resources," Socio-Economic Planning Sciences, Elsevier, vol. 32(4), pages 257-263, December.
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    4. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, January.
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    2. Kaplan, Edward H., 2013. "Staffing models for covert counterterrorism agencies," Socio-Economic Planning Sciences, Elsevier, vol. 47(1), pages 2-8.
    3. Perea, Federico & Puerto, Justo, 2013. "Revisiting a game theoretic framework for the robust railway network design against intentional attacks," European Journal of Operational Research, Elsevier, vol. 226(2), pages 286-292.
    4. Wang, Xiaofang & Zhuang, Jun, 2011. "Balancing congestion and security in the presence of strategic applicants with private information," European Journal of Operational Research, Elsevier, vol. 212(1), pages 100-111, July.
    5. Meyer Sunniva F., 2011. "Preventing Mass Killings: Determining the Optimal Allocation of Security Resources between Crowded Targets," Peace Economics, Peace Science, and Public Policy, De Gruyter, vol. 17(1), pages 1-37, September.
    6. Deutsch, Yael & Golany, Boaz & Rothblum, Uriel G., 2011. "Determining all Nash equilibria in a (bi-linear) inspection game," European Journal of Operational Research, Elsevier, vol. 215(2), pages 422-430, December.
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    8. Hendel, Ulrich, 2012. ""Look like the innocent flower, but be the serpent under't": Mimicking behaviour of growth-oriented terrorist organizations," Discussion Papers in Economics 13998, University of Munich, Department of Economics.
    9. Wenzel, Lars & Wolf, André, 2013. "Protection against major catastrophes: An economic perspective," HWWI Research Papers 137, Hamburg Institute of International Economics (HWWI).
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    11. Jessica L. Heier Stamm & Nicoleta Serban & Julie Swann & Pascale Wortley, 2017. "Quantifying and explaining accessibility with application to the 2009 H1N1 vaccination campaign," Health Care Management Science, Springer, vol. 20(1), pages 76-93, March.
    12. Shan, Xiaojun & Zhuang, Jun, 2013. "Hybrid defensive resource allocations in the face of partially strategic attackers in a sequential defender–attacker game," European Journal of Operational Research, Elsevier, vol. 228(1), pages 262-272.
    13. Michael Brzoska & Raphael Bossong & Eric van Um, 2011. "Security Economics in the European Context: Implications of the EUSECON Project," Economics of Security Working Paper Series 58, DIW Berlin, German Institute for Economic Research.
    14. repec:eee:reensy:v:165:y:2017:i:c:p:292-301 is not listed on IDEAS
    15. Paulson, Elisabeth C. & Linkov, Igor & Keisler, Jeffrey M., 2016. "A game theoretic model for resource allocation among countermeasures with multiple attributes," European Journal of Operational Research, Elsevier, vol. 252(2), pages 610-622.
    16. Nikoofal, Mohammad E. & Zhuang, Jun, 2015. "On the value of exposure and secrecy of defense system: First-mover advantage vs. robustness," European Journal of Operational Research, Elsevier, vol. 246(1), pages 320-330.
    17. Schmitt, Amanda J. & Snyder, Lawrence V. & Shen, Zuo-Jun Max, 2010. "Inventory systems with stochastic demand and supply: Properties and approximations," European Journal of Operational Research, Elsevier, vol. 206(2), pages 313-328, October.
    18. Haphuriwat, N. & Bier, V.M., 2011. "Trade-offs between target hardening and overarching protection," European Journal of Operational Research, Elsevier, vol. 213(1), pages 320-328, August.


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