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Resource allocation among multiple targets for a defender-attacker game with false targets consideration

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  • Zhang, Xiaoxiong
  • Ding, Song
  • Ge, Bingfeng
  • Xia, Boyuan
  • Pedrycz, Witold

Abstract

Appropriate resource allocation among multiple targets plays a vital role in the defender-attacker game. Traditional methods seldom consider the optimal resource allocation with more than one strategy among multiple targets. Accordingly, we assume that the defender moves first, allocating resources in deploying different false targets and strengthening the genuine ones among multiple targets. The attacker moves after observing the defender's move, distributing resources in identifying false targets and then attacking the genuine ones concerning multiple targets. Each player aims to maximize their own overall expected utility given any of the other player's move. The optimal resource distribution between target intelligence/protection for the defender and target identification/attack efforts among multiple targets for the attacker is studied. We model and obtain analytical equilibrium results under various parameter settings. Our results show that increased intelligence (impact) contest intensities lead to lower (higher) attacker resources in intelligence (attack). Moreover, the zero-sum game where both players share the same preferences without additional payoff consideration results in the worst losses for the defender. The forgoing method offers an original way to approach the resource allocation problems in security defense fields.

Suggested Citation

  • Zhang, Xiaoxiong & Ding, Song & Ge, Bingfeng & Xia, Boyuan & Pedrycz, Witold, 2021. "Resource allocation among multiple targets for a defender-attacker game with false targets consideration," Reliability Engineering and System Safety, Elsevier, vol. 211(C).
  • Handle: RePEc:eee:reensy:v:211:y:2021:i:c:s0951832021001617
    DOI: 10.1016/j.ress.2021.107617
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    References listed on IDEAS

    as
    1. Xiaojun Shan & Jun Zhuang, 2013. "Cost of Equity in Homeland Security Resource Allocation in the Face of a Strategic Attacker," Risk Analysis, John Wiley & Sons, vol. 33(6), pages 1083-1099, June.
    2. Gregory Levitin & Kjell Hausken, 2009. "Intelligence and Impact Contests in Systems with Fake Targets," Defense & Security Analysis, Taylor & Francis Journals, vol. 25(2), pages 157-173, June.
    3. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
    4. Zhiheng Xu & Jun Zhuang, 2019. "A Study on a Sequential One‐Defender‐N‐Attacker Game," Risk Analysis, John Wiley & Sons, vol. 39(6), pages 1414-1432, June.
    5. 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.
    6. Vicki Bier & Santiago Oliveros & Larry Samuelson, 2007. "Choosing What to Protect: Strategic Defensive Allocation against an Unknown Attacker," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 9(4), pages 563-587, August.
    7. Levitin, Gregory & Hausken, Kjell, 2009. "False targets efficiency in defense strategy," European Journal of Operational Research, Elsevier, vol. 194(1), pages 155-162, April.
    8. 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.
    9. 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).
    10. Peiqiu Guan & Meilin He & Jun Zhuang & Stephen C. Hora, 2017. "Modeling a Multitarget Attacker–Defender Game with Budget Constraints," Decision Analysis, INFORMS, vol. 14(2), pages 87-107, June.
    11. Zhang, Jing & Zhuang, Jun & Jose, Victor Richmond R., 2018. "The role of risk preferences in a multi-target defender-attacker resource allocation game," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 95-104.
    12. Hausken, Kjell & Levitin, Gregory, 2009. "Protection vs. false targets in series systems," Reliability Engineering and System Safety, Elsevier, vol. 94(5), pages 973-981.
    13. Jie Xu & Jun Zhuang, 2016. "Modeling costly learning and counter-learning in a defender-attacker game with private defender information," Annals of Operations Research, Springer, vol. 236(1), pages 271-289, January.
    14. Xiaoxiong Zhang & Keith W. Hipel & Bingfeng Ge & Yuejin Tan, 2019. "A game‐theoretic model for resource allocation with deception and defense efforts," Systems Engineering, John Wiley & Sons, vol. 22(3), pages 282-291, May.
    15. Levitin, Gregory & Hausken, Kjell, 2009. "Intelligence and impact contests in systems with redundancy, false targets, and partial protection," Reliability Engineering and System Safety, Elsevier, vol. 94(12), pages 1927-1941.
    16. 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.
    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. Di Wu & Xiangbin Yan & Rui Peng & Shaomin Wu, 2020. "Optimal defence-attack strategies between one defender and two attackers," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 71(11), pages 1830-1846, November.
    19. Levitin, Gregory & Hausken, Kjell, 2013. "Is it wise to leave some false targets unprotected?," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 176-186.
    20. Zhang, Jing & Wang, Yan & Zhuang, Jun, 2021. "Modeling multi-target defender-attacker games with quantal response attack strategies," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    21. Peng, R. & Zhai, Q.Q. & Levitin, G., 2016. "Defending a single object against an attacker trying to detect a subset of false targets," Reliability Engineering and System Safety, Elsevier, vol. 149(C), pages 137-147.
    22. 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.
    23. Shan, Xiaojun & Zhuang, Jun, 2018. "Modeling cumulative defensive resource allocation against a strategic attacker in a multi-period multi-target sequential game," Reliability Engineering and System Safety, Elsevier, vol. 179(C), pages 12-26.
    24. Zhuang, Jun & Bier, Vicki M. & Alagoz, Oguzhan, 2010. "Modeling secrecy and deception in a multiple-period attacker-defender signaling game," European Journal of Operational Research, Elsevier, vol. 203(2), pages 409-418, June.
    25. Zhang, Xiaoxiong & Ye, Yanqing & Tan, Yuejin, 2020. "How to protect a genuine target against an attacker trying to detect false targets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    26. Kjell Hausken, 2019. "Defence and attack of complex interdependent systems," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 70(3), pages 364-376, March.
    27. R Peng & G Levitin & M Xie & S H Ng, 2011. "Optimal defence of single object with imperfect false targets," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(1), pages 134-141, January.
    28. 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.
    29. 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).
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