A Cumulative Prospect Theory Based Counterterrorism Resource Allocation Method under Interval Values

Abstract

Strategic resource allocation into decision-making model plays a valuable role for the defender in mitigating damage and improving efficiency in military environments. In this paper, we develop a defensive resource allocation model based on cumulative prospect theory (CPT), which considers terrorists’ psychological factors of decision-making in reality. More specifically, we extend existing models in the presence of multiple attributes and terrorists’ deviations from rationality using a multi-attribute cumulative prospect theory. In addition, interval values are used to cope with uncertainties regarding gain and loss. Comparative studies are also carried out to demonstrate the differences among minmax, Nash eguilibrium (NE), and traditional probability risk analysis (PRA) strategies. Results show that the defender’s optimal defensive resource allocation will change along with terrorists’ behaviors and the proposed model makes more sense compared with other traditional resource allocation strategies.

Keywords

Counterterrorism resource allocation / cumulative prospect theory / multiple attributes / interval value

References

[1] Abdellaoui M. Parameter-free elicitation of utility and probability weighting functions. Management Science, 2000, 46(11): 1497-1512.

[2] Baillon A, Bleichrodt H, Keskin U, L’Haridon O, Li C. Learning under Ambiguity: An Experiment Using Initial Public Offerings on a Stock Market.. Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS, 2013 2013-31.

[3] Bleichrodt H, Pinto JL. A parameter-free elicitation of the probability weighting function in medical decision analysis. Management Science, 2000, 46(11): 1485-1496.

[4] Bleichrodt H, Schmidt U, Zank H. Additive utility in prospect theory. Management Science, 2009, 55(5): 863-873.

[5] Bromiley P. A prospect theory model of resource allocation. Decision Analysis, 2009, 6(3): 124-138.

[6] Chateauneuf A, Eichberger J, Grant S. Choice under uncertainty with the best and worst in mind: Neoadditive capacities. Journal of Economic Theory, 2007, 137(1): 538-567.

[7] Fleurbaey M, Maniquet F. Optimal income taxation theory and principles of fairness. Journal of Economic Literature, 2018, 56(3): 1029-1079.

[8] Golany B, Goldberg N, Rothblum UG. A two-resource allocation algorithm with an application to large-scale zero-sum defensive games. Computers & Operations Research, 2017, 78: 218-229.

[9] Guan P, He M, Zhuang J, Hora SC. Modeling a multitarget attacker-defender game with budget constraints. Decision Analysis, 2017, 14(2): 87-107.

[10] Jiao Y, Luo Z. A model of terrorism and counterter-rorism with location choices. Public Choice, 2019, 179(3): 301-313.

[11] Kahneman D, Tversky A. Prospect theory: An analysis of decision under risk. Econometrica, 1979, 47(2): 263-292.

[12] Kujawski E. Accounting for terrorist behavior in allocating defensive counterterrorism resources. Systems Engineering, 2015, 18(4): 365-376.

[13] Liu Y, Fan ZP, Zhang Y. Risk decision analysis in emergency response: A method based on cumulative prospect theory. Computers & Operations Research, 2014, 42: 75-82.

[14] Mazicioglu D, Merrick JRW. Behavioral modeling of adversaries with multiple objectives in counterterrorism. Risk Analysis, 2018, 38(5): 962-977.

[15] Paulson EC, Linkov I, Keisier JM. A game theoretic model for resource allocation among countermeasures with multiple attributes. European Journal of Operational Research, 2016, 252(2): 610-622.

[16] Phillips PJ, Pohl G. Terrorist choice: A stochastic dominance and prospect theory analysis. Defence and Peace Economics, 2017, 28(2): 150-164.

[17] Quiggin J. Comparative staties for rank-dependent expected utility theory. Journal of Risk and Uncertainty, 1991, 4(4): 339-350.

[18] Samuel A, Guikema SD. Resource allocation for homeland defense: Dealing with the team effect. Decision Analysis, 2012, 9(3): 238-252.

[19] Shan X, Zhuang J. Hybrid defensive resource allocations in the face of partially strategie attackers in a sequential defender-attacker game. European Journal of Operational Research, 2013, 228(1): 262-272.

[20] Shan X, Zhuang J. Cost of equity in homeland security resource allocation in the face of a strategie attacker. Risk Analysis, 2013, 33(6): 1083-1099.

[21] Shan X, Zhuang J. Modeling cumulative defensive resource allocation against a strategie attacker in a multi-period multi-target sequential game. Reliability Engineering & System Safety, 2018, 179(SI): 12-26.

[22] Train KE. Discrete Choice Methods with Simula-tioniled)., 2009, Berkeley.: Cambridge University Press.

[23] Tversky A, Kahneman D. Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty, 1992, 5(4): 297-323.

[24] Von Neumann J, Morgenstern O. Theory of Games and Economie Behavior., 1944, Princeton: Princeton University Press.

[25] Wang C, Bier VM. Expert elicitation of adversary preferences using ordinal judgments. Operations Research, 2013, 61(2): 372-385.

[26] Wang L, Zhang ZX, Wang YM. A prospect theorybased interval dynamic reference point method for emergency decision making. Expert Systems with Applications, 2015, 42(23): 9379-9388.

[27] Wang L, Wang YM, Martinez L. A group decision method based on prospect theory for emergency situations. Information Sciences, 2017, 418–419: 119-135.

[28] Willis HH. Guiding resource allocations based on terrorism risk. Risk Analysis, 2007, 27(3): 597-606.

[29] Yang R, Kiekintveld C, Ordónez F, Tambe M, John R. Improving resource allocation strategies against human adversaries in security games: An extended study. Artificial Intelligence, 2013, 195: 440-469.

[30] Yang L, Wang G, Chai Y. Manufacturer’s channel selection considering carbon emission reduction and remanufacturing. Journal of Systems Science and Systems Engineering, 2018, 27(4): 497-518.

[31] Zhang X, Ge B, Jiang J, Tan Y. Consensus building in group decision making based on multiplicative consistency with incomplete reciprocal preference relations. Knowledge-Based Systems, 2016, 106: 96-104.

[32] Zhang S, Zhu J, Liu X, Chen Y. Regret theory-based group decision-making with multidimensional preference and incomplete weight information. Information Fusion, 2016, 31: 1-13.

[33] Zhang X, Hipel KW, Ge B, Tan Y. A game-theoretic model for resource allocation with deception and defense efforts. Systems Engineering, 2019, 22(3): 282-291.

[34] Zhu J, Ma Z, Wang H, Chen Y. Risk decision-making method using interval numbers and its application based on the prospect value with multiple reference points. Information Sciences, 2017 385-386.

[35] Zhuang J, Bier VM. Balancing terrorism and natural disasters - Defensive strategy with endogenous attacker effort. Operations Research, 2007, 55(5): 976-991.