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Optimal defense-attack strategies between M defenders and N attackers: A method based on cumulative prospect theory

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  • Lin, Chen
  • Xiao, Hui
  • Peng, Rui
  • Xiang, Yisha

Abstract

This research studies the system defense of M defenders against N attackers. We model this problem as a defense-attack game between M defenders and N attackers based on the cumulative prospect theory. In this game, the defenders can allocate their resources to defend the system from being attacked, and to attack the attackers such that the opponents lose their offensive power. In response, the attackers can allocate its offensive resources to attack the system and defend themselves from being attacked by the defenders. In this research, we use the cumulative prospect value instead of the vulnerability as the performance measure such that the risk attitudes of defenders and attackers can be considered. Further, we study the cooperative behaviors and non-cooperative behaviors of the attackers and analyze the effect on the optimal resource allocation. Numerical experiments are carried out to illustrate the applications.

Suggested Citation

  • Lin, Chen & Xiao, Hui & Peng, Rui & Xiang, Yisha, 2021. "Optimal defense-attack strategies between M defenders and N attackers: A method based on cumulative prospect theory," Reliability Engineering and System Safety, Elsevier, vol. 210(C).
    • Handle: RePEc:eee:reensy:v:210:y:2021:i:c:s0951832021000727
    DOI: 10.1016/j.ress.2021.107510
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    as
    1. Kjell Hausken, 2017. "Information Sharing Among Cyber Hackers in Successive Attacks," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(02), pages 1-33, June.
    2. Ulrich Schmidt & Horst Zank, 2008. "Risk Aversion in Cumulative Prospect Theory," Management Science, INFORMS, vol. 54(1), pages 208-216, January.
    3. Bier, Vicki & Gutfraind, Alexander, 2019. "Risk analysis beyond vulnerability and resilience – characterizing the defensibility of critical systems," European Journal of Operational Research, Elsevier, vol. 276(2), pages 626-636.
    4. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    5. Zambrano, Eduardo, 2020. "Risk attitudes over small and large stakes recalibrated," Economics Letters, Elsevier, vol. 187(C).
    6. Gao, Kaiye & Yan, Xiangbin & Liu, Xiang-dong & Peng, Rui, 2019. "Object defence of a single object with preventive strike of random effect," Reliability Engineering and System Safety, Elsevier, vol. 186(C), pages 209-219.
    7. Booij, Adam S. & van de Kuilen, Gijs, 2009. "A parameter-free analysis of the utility of money for the general population under prospect theory," Journal of Economic Psychology, Elsevier, vol. 30(4), pages 651-666, August.
    8. Mohsen Golalikhani & Jun Zhuang, 2011. "Modeling Arbitrary Layers of Continuous‐Level Defenses in Facing with Strategic Attackers," Risk Analysis, John Wiley & Sons, vol. 31(4), pages 533-547, April.
    9. Wu, Di & Xiao, Hui & Peng, Rui, 2018. "Object defense with preventive strike and false targets," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 76-80.
    10. Wu, Di & Yan, Xiangbin & Peng, Rui & Wu, Shaomin, 2020. "Risk-attitude-based defense strategy considering proactive strike, preventive strike and imperfect false targets," Reliability Engineering and System Safety, Elsevier, vol. 196(C).
    11. Kjell Hausken, 2010. "Risk, production and conflict when utilities are as if certain," International Journal of Decision Sciences, Risk and Management, Inderscience Enterprises Ltd, vol. 2(3/4), pages 228-251.
    12. Ye, Zhi-Sheng & Peng, Rui & Wang, Wenbin, 2017. "Defense and attack of performance-sharing common bus systemsAuthor-Name: Zhai, Qingqing," European Journal of Operational Research, Elsevier, vol. 256(3), pages 962-975.
    13. Dui, Hongyan & Si, Shubin & Wu, Shaomin & Yam, Richard C.M., 2017. "An importance measure for multistate systems with external factors," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 49-57.
    14. Levitin, Gregory & Hausken, Kjell, 2009. "False targets efficiency in defense strategy," European Journal of Operational Research, Elsevier, vol. 194(1), pages 155-162, April.
    15. Levitin, Gregory & Xing, Liudong & Xiang, Yanping, 2020. "Optimal early warning defense of N-version programming service against co-resident attacks in cloud system," Reliability Engineering and System Safety, Elsevier, vol. 201(C).
    16. Peng, Rui & Wu, Di & Xiao, Hui & Xing, Liudong & Gao, Kaiye, 2019. "Redundancy versus protection for a non-reparable phased-mission system subject to external impacts," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    17. Zhang, Jing & Zhuang, Jun, 2019. "Modeling a multi-target attacker-defender game with multiple attack types," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 465-475.
    18. Rui Peng & Min Xie & Szu Ng & Gregory Levitin, 2012. "Element maintenance and allocation for linear consecutively connected systems," IISE Transactions, Taylor & Francis Journals, vol. 44(11), pages 964-973.
    19. Qingqing Zhai & Rui Peng & Jun Zhuang, 2020. "Defender–Attacker Games with Asymmetric Player Utilities," Risk Analysis, John Wiley & Sons, vol. 40(2), pages 408-420, February.
    20. Szidarovszky, Ferenc & Luo, Yi, 2014. "Incorporating risk seeking attitude into defense strategy," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 104-109.
    21. Hausken, Kjell & Bier, Vicki M., 2011. "Defending against multiple different attackers," European Journal of Operational Research, Elsevier, vol. 211(2), pages 370-384, June.
    22. Xiao, Hui & Lin, Chen & Kou, Gang & Peng, Rui, 2020. "Optimal resource allocation for defending k-out-of-n systems against sequential intentional and unintentional impacts," Reliability Engineering and System Safety, Elsevier, vol. 201(C).
    23. Mohammed Abdellaoui & Han Bleichrodt & Corina Paraschiv, 2007. "Loss Aversion Under Prospect Theory: A Parameter-Free Measurement," Management Science, INFORMS, vol. 53(10), pages 1659-1674, October.
    24. Shan, Xiaojun Gene & Zhuang, Jun, 2020. "A game-theoretic approach to modeling attacks and defenses of smart grids at three levels," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    25. Yang, Li & Ye, Zhi-sheng & Lee, Chi-Guhn & Yang, Su-fen & Peng, Rui, 2019. "A two-phase preventive maintenance policy considering imperfect repair and postponed replacement," European Journal of Operational Research, Elsevier, vol. 274(3), pages 966-977.
    26. Liu, Yu & Chen, Yiming & Jiang, Tao, 2020. "Dynamic selective maintenance optimization for multi-state systems over a finite horizon: A deep reinforcement learning approach," European Journal of Operational Research, Elsevier, vol. 283(1), pages 166-181.
    27. Levitin, Gregory & Hausken, Kjell, 2011. "Preventive strike vs. false targets and protection in defense strategy," Reliability Engineering and System Safety, Elsevier, vol. 96(8), pages 912-924.
    28. Xufeng Zhao & Satoshi Mizutani & Toshio Nakagawa, 2017. "Replacement policies for age and working numbers with random life cycle," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(14), pages 6791-6802, July.
    29. Jindapon, Paan & Yang, Zhe, 2017. "Risk attitudes and heterogeneity in simultaneous and sequential contests," Journal of Economic Behavior & Organization, Elsevier, vol. 138(C), pages 69-84.
    30. Bose, Gautam & Konrad, Kai A., 2020. "Devil take the hindmost: Deflecting attacks to other defenders," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    31. Kjell Hausken, 2017. "Security Investment, Hacking, and Information Sharing between Firms and between Hackers," Games, MDPI, vol. 8(2), pages 1-23, May.
    32. Peng, Rui & Xiao, Hui & Guo, Jianjun & Lin, Chen, 2020. "Defending a parallel system against a strategic attacker with redundancy, protection and disinformation," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    33. Peng, R. & Levitin, G. & Xie, M. & Ng, S.H., 2010. "Defending simple series and parallel systems with imperfect false targets," Reliability Engineering and System Safety, Elsevier, vol. 95(6), pages 679-688.
    34. Feng, Qilin & Cai, Hao & Chen, Zhilong, 2019. "Using game theory to optimize the allocation of defensive resources on a city scale to protect chemical facilities against multiple types of attackers," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    35. Levitin, Gregory & Hausken, Kjell & Dai, Yuanshun, 2014. "Optimal defense with variable number of overarching and individual protections," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 81-90.
    36. Bostick, T.P. & Connelly, E.B. & Lambert, J.H. & Linkov, I., 2018. "Resilience science, policy and investment for civil infrastructure," Reliability Engineering and System Safety, Elsevier, vol. 175(C), pages 19-23.
    37. Mohammed Abdellaoui, 2000. "Parameter-Free Elicitation of Utility and Probability Weighting Functions," Management Science, INFORMS, vol. 46(11), pages 1497-1512, November.
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    5. Li, Qing & Li, Mingchu & Gong, Zhongqiang & Tian, Yuan & Zhang, Runfa, 2022. "Locating and protecting interdependent facilities to hedge against multiple non-cooperative limited choice attackers," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
    6. Hunt, Kyle & Zhuang, Jun, 2024. "A review of attacker-defender games: Current state and paths forward," European Journal of Operational Research, Elsevier, vol. 313(2), pages 401-417.
    7. Konrad, Kai A. & Morath, Florian, 2023. "How to preempt attacks in multi-front conflict with limited resources," European Journal of Operational Research, Elsevier, vol. 305(1), pages 493-500.
    8. Li, Yulong & Lin, Jie & Zhang, Chi & Zhu, Huaxing & Zeng, Saixing & Sun, Chengshaung, 2022. "Joint optimization of structure and protection of interdependent infrastructure networks," Reliability Engineering and System Safety, Elsevier, vol. 218(PB).
    9. Chaoqi, Fu & Yangjun, Gao & Jilong, Zhong & Yun, Sun & Pengtao, Zhang & Tao, Wu, 2021. "Attack-defense game for critical infrastructure considering the cascade effect," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    10. Hunt, Kyle & Agarwal, Puneet & Zhuang, Jun, 2022. "On the adoption of new technology to enhance counterterrorism measures: An attacker–defender game with risk preferences," Reliability Engineering and System Safety, Elsevier, vol. 218(PB).

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