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Multifirm models of cybersecurity investment competition vs. cooperation and network vulnerability

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  • Nagurney, Anna
  • Shukla, Shivani

Abstract

In this paper, we develop and compare three distinct models for cybersecurity investment in competitive and cooperative situations to safeguard against potential and ongoing threats. We introduce a Nash equilibrium model of noncooperation in terms of cybersecurity levels of the firms involved, which is formulated, analyzed, and solved using variational inequality theory. The equilibrium of this model then acts as the disagreement point over which bargaining takes place in the setting of the second model, which yields a cooperative solution in which the firms are guaranteed that their expected utilities are no lower than those achieved under noncooperation. Nash bargaining theory is utilized to argue for information sharing and to quantify its monetary and security benefits in terms of reduction in network vulnerability to cyberattacks. The third model in this paper also focuses on cooperation among the firms in terms of their cybersecurity levels, but from a system-optimization perspective in which the sum of the expected utilities is maximized. Qualitative properties are provided for the models in terms of existence and uniqueness results along with numerical solutions to two cases focusing on retailers and financial service firms, since these have been subject to some of the most damaging cyberattacks. Sensitivity analysis results are also provided. We compare the solutions of the models for the cases and recommend a course of action that has both financial and policy-related implications.

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  • Nagurney, Anna & Shukla, Shivani, 2017. "Multifirm models of cybersecurity investment competition vs. cooperation and network vulnerability," European Journal of Operational Research, Elsevier, vol. 260(2), pages 588-600.
    • Handle: RePEc:eee:ejores:v:260:y:2017:i:2:p:588-600
    DOI: 10.1016/j.ejor.2016.12.034
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    2. Zhou, Yan & Chan, Chi Kin & Wong, Kar Hung, 2018. "A multi-period supply chain network equilibrium model considering retailers’ uncertain demands and dynamic loss-averse behaviors," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 118(C), pages 51-76.
    3. Da, Gaofeng & Xu, Maochao & Zhao, Peng, 2021. "Multivariate dependence among cyber risks based on L-hop propagation," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 525-546.
    4. Suyuan Luo & Tsan‐Ming Choi, 2022. "E‐commerce supply chains with considerations of cyber‐security: Should governments play a role?," Production and Operations Management, Production and Operations Management Society, vol. 31(5), pages 2107-2126, May.
    5. Li, Jianbin & Luo, Xiaomeng & Wang, Qifei & Zhou, Weihua, 2021. "Supply chain coordination through capacity reservation contract and quantity flexibility contract," Omega, Elsevier, vol. 99(C).
    6. Hausken, Kjell, 2024. "Fifty Years of Operations Research in Defense," European Journal of Operational Research, Elsevier, vol. 318(2), pages 355-368.
    7. Guizhou Wang & Jonathan W. Welburn & Kjell Hausken, 2020. "A Two-Period Game Theoretic Model of Zero-Day Attacks with Stockpiling," Games, MDPI, vol. 11(4), pages 1-26, December.
    8. Chan, Chi Kin & Zhou, Yan & Wong, Kar Hung, 2019. "An equilibrium model of the supply chain network under multi-attribute behaviors analysis," European Journal of Operational Research, Elsevier, vol. 275(2), pages 514-535.
    9. Zhang, Xiaoyu & Xu, Maochao & Su, Jianxi & Zhao, Peng, 2023. "Structural models for fog computing based internet of things architectures with insurance and risk management applications," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1273-1291.
    10. Alessandro Mazzoccoli & Maurizio Naldi, 2021. "Optimal Investment in Cyber-Security under Cyber Insurance for a Multi-Branch Firm," Risks, MDPI, vol. 9(1), pages 1-28, January.
    11. Simon, Jay & Omar, Ayman, 2020. "Cybersecurity investments in the supply chain: Coordination and a strategic attacker," European Journal of Operational Research, Elsevier, vol. 282(1), pages 161-171.
    12. Eling, Martin & Wirfs, Jan, 2019. "What are the actual costs of cyber risk events?," European Journal of Operational Research, Elsevier, vol. 272(3), pages 1109-1119.
    13. Caruso, Valeria & Daniele, Patrizia, 2018. "A network model for minimizing the total organ transplant costs," European Journal of Operational Research, Elsevier, vol. 266(2), pages 652-662.
    14. Chan, Chi Kin & Zhou, Yan & Wong, Kar Hung, 2018. "A dynamic equilibrium model of the oligopolistic closed-loop supply chain network under uncertain and time-dependent demands," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 118(C), pages 325-354.
    15. Berlilana & Tim Noparumpa & Athapol Ruangkanjanases & Taqwa Hariguna & Sarmini, 2021. "Organization Benefit as an Outcome of Organizational Security Adoption: The Role of Cyber Security Readiness and Technology Readiness," Sustainability, MDPI, vol. 13(24), pages 1-20, December.
    16. Lu Xu & Yanhui Li & Jing Fu, 2019. "Cybersecurity Investment Allocation for a Multi-Branch Firm: Modeling and Optimization," Mathematics, MDPI, vol. 7(7), pages 1-20, July.
    17. Paul, Jomon A. & Zhang, Minjiao, 2021. "Decision support model for cybersecurity risk planning: A two-stage stochastic programming framework featuring firms, government, and attacker," European Journal of Operational Research, Elsevier, vol. 291(1), pages 349-364.

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