Choosing what to protect when attacker resources and asset valuations are uncertain

• Autorzy: Hausken K.

Identyfikatory

DOI

10.5277/ord140302

• Języki publikacji: EN

Abstrakty

EN

The situation has been modelled where the attacker’s resources are unknown to the defender. Protecting assets presupposes that the defender has some information on the attacker’s resource capabilities. An attacker targets one of two assets. The attacker’s resources and valuations of these assets are drawn probabilistically. We specify when the isoutility curves are upward sloping (the defender prefers to invest less in defense, thus leading to higher probabilities of success for attacks on both assets) or downward sloping (e.g. when one asset has a low value or high unit defense cost). This stands in contrast to earlier research and results from the uncertainty regarding the level of the attacker’s resources. We determine which asset the attacker targets depending on his type, unit attack costs, the contest intensity, and investment in defense. A two stage game is considered, where the defender moves first and the attacker moves second. When both assets are equivalent and are treated equivalently by both players, an interior equilibrium exists when the contest intensity is low, and a corner equilibrium with no defense exists when the contest intensity is large and the attacker holds large resources. Defense efforts are inverse U shaped in the attacker’s resources.

Słowa kluczowe

EN

assets; defense; attack; game theory; uncertainty; resources; valuations; contest success function; optimization

PL

majątek; obrona; atak; teoria gier; niepewność; zasoby; wyceny; optymalizacja

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Operations Research and Decisions
• Rocznik: 2014
• Tom: Vol. 24, No. 3
• Strony: 23--44
• Opis fizyczny: Bibliogr. 32 poz., rys.

Twórcy

autor

Hausken K.

• Faculty of Social Sciences, University of Stavanger, 4036 Stavanger, Norway

Bibliografia

• [1] ARCE D.G., SANDLER T., Counterterrorism: A game theoretic analysis, Journal of Conflict Resolution, 2005, 49, 183–200.
• [2] BERNHARDT D., POLBORN M.P., Non-convexities and the gains from concealing defenses from committed terrorists, Economics Letters, 2010, 107 (1), 52–54.
• [3] BIER V.M., NAGARAJ A., ABHICHANDANI V., Protection of simple series and parallel systems with components of different values, Reliability Engineering and System Safety, 2005, 87 (3), 315–323.
• [4] BIER V.M., OLIVEROS S., SAMUELSON L., Choosing what to protect: strategic defense allocation against an unknown attacker, Journal of Public Economic Theory, 2007, 9 (4), 563–587.
• [5] 40 years of rent seeking, Vols. 1, 2, R.D. Congleton, A.L. Hillman, K.A. Konrad (Eds.), Springer, Berlin 2008.
• [6] DIGHE N., ZHUANG J., BIER V.M., Secrecy in defensive allocations as a strategy for achieving more cost-effective attacker deterrence, International Journal of Performability Engineering, 2009, 5 (1), 31–43.
• [7] FEY M., Rent-seeking contests with incomplete information, Public Choice, 2008, 135 (3–4), 225–236.
• [8] FREY B.S., LUECHINGER S., How to fight terrorism: Alternatives to deterrence, Defence and Peace Economics, 2003, 14, 237–249.
• [9] GOLMAN R., PAGE S.E., General blotto. Games of allocative strategic mismatch, Public Choice, 2009, 138 (3–4), 279–299.
• [10] GORDON L.A., LOEB M.P., Managing Cybersecurity Resources: A Cost-Benefit Analysis, McGraw--Hill, Inc., New York 2006.
• [11] HAUSKEN K., On the impossibility of deterrence in sequential colonel blotto games, International Game Theory Review, 2012, 14 (2), 1–13.
• [12] HAUSKEN K., BIER V., ZHUANG J., Defending against terrorism, natural disaster, and all hazards, [in:] V.M. Bier, M.N. Azaiez (Eds.), Game Theoretic Risk Analysis of Security Threats, Springer, New York 2009, 65–97.
• [13] HAUSKEN K., LEVITIN G., Review of systems defense and attack models, International Journal of Performability Engineering, 2012, 8 (4), 355–366.
• [14] HAUSKEN K., ZHUANG J., Defending Against a Terrorist Who Accumulates Resources, Military Operations Research, 2011, 16 (1), 21–39.
• [15] KUNREUTHER H., HEAL G., Interdependent security, The Journal of Risk and Uncertainty, 2003, 26, (2/3), 231–249.
• [16] LEVITIN G., HAUSKEN K., False targets efficiency in defense strategy, European Journal of OperationalResearch, 2009, 194 (1), 155–162.
• [17] LEVITIN G., HAUSKEN K., Is it wise to leave some false targets unprotected? Reliability Engineering and System Safety, 2013, 112, 176–186.
• [18] NIKOOFAL M., ZHUANG J., Robust allocation of a defensive budget considering an attacker’s private information, Risk Analysis, 2012, 32 (5), 930–943.
• [19] POWELL R., Allocating defensive resources with private information about vulnerability, American Political Science Review, 2007, 101 (4), 799–809.
• [20] POWELL R., Defending against terrorist attacks with limited resources, American Political Science Review, 2007, 101 (3), 527–541.
• [21] POWELL R., Sequential, nonzero-sum Blotto. Allocating defensive resources prior to attack, Games and Economic Behavior, 2009, 67 (2), 611–615.
• [22] SANDLER T., LAPAN H.E., The calculus of dissent: An analysis of terrorists’ choice of targets, Synthese, 1988, 76, 245–261.
• [23] SANDLER T., SIQUEIRA K., Games and terrorism: recent developments, Simulation and Gaming, 2009, 40 (2), 164–192.
• [24] SHAN X., ZHUANG J., Cost of equity in homeland security resource allocation in the face of a strategic attacker, Risk Analysis, 2013, 33 (6), 1083–1099.
• [25] SHAN X., ZHUANG J., Hybrid defensive resource allocations in the face of partially strategic attackers in a sequential defender–attacker game, European Journal of Operational Research, 2013, 228 (1), 262–272.
• [26] SKAPERDAS S., Contest success functions, Economic Theory, 1996, 7, 283–290.
• [27] TULLOCK G., Efficient rent-seeking, [in:] J.M. Buchanan, R.D. Tollison, G. Tullock, Toward a theory of the rent-seeking society, Texas A. & M. University Press, College Station, 1980, 97–112.
• [28] ZHUANG J., BIER V.M., ALAGOZ O., Modeling secrecy and deception in a multiple-period attacker –defender signaling game, European Journal of Operational Research, 2010, 203 (2), 409–418.
• [29] ZHUANG J., BIER V., Balancing terrorism and natural disasters: Defensive strategy with endogenous attacker effort, Operations Research, 2007, 55 (5), 976–991.
• [30] ZHUANG J., BIER V.M., Reasons for secrecy and deception in homeland security. Resource allocation, Risk Analysis, 2010, 30 (12), 1737–1743.
• [31] ZHUANG J., BIER V.M., Secrecy and deception at equilibrium, with applications to anti-terrorism resource allocation, Defence and Peace Economics, 2011, 22 (1), 43–61.
• [32] WANG X., ZHUANG J., Balancing congestion and security in the presence of strategic applicants with private information, European Journal of Operational Research, 2011, 212 (1), 100–111.