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Robust Adversarial Risk Analysis: A Level- k Approach

Author

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  • Laura McLay

    (Department of Statistical Sciences and Operations Research, Virginia Commonwealth University, Richmond, Virginia 23284)

  • Casey Rothschild

    (Department of Economics, Wellesley College, Wellesley, Massachusetts 02481)

  • Seth Guikema

    (Department of Geography and Environmental Engineering, Johns Hopkins University, Baltimore, Maryland 21318)

Abstract

Adversarial risk analysis is an active and important area of decision analytic research. Both single-actor decision analysis and multiple-actor game theory have been applied to this problem, with game theoretic methods being particularly popular. Although game theory models do explicitly capture strategic interactions between attackers and defenders, two of the key assumptions---decision making based on subjective expected utility maximization and common knowledge of rationality---are known to be descriptively inaccurate in some situations. This paper addresses these shortcomings by proposing, formulating, and illustrating the application of robust optimization methodologies to a level- k game theory model for adversarial risk analysis. Level- k game theory provides a practical method for modeling bounded rationality. Robust optimization provides an alternative way to model the actions of conservative players facing “deep” uncertainties about their environment---uncertainties that are possible to bound but that are difficult or impossible to represent using probability distributions. Our approach thus combines level- k and robust optimization insights to provide a computationally tractable model of boundedly rational players who are faced with significant and difficult to quantify uncertainties.

Suggested Citation

  • Laura McLay & Casey Rothschild & Seth Guikema, 2012. "Robust Adversarial Risk Analysis: A Level- k Approach," Decision Analysis, INFORMS, vol. 9(1), pages 41-54, March.
  • Handle: RePEc:inm:ordeca:v:9:y:2012:i:1:p:41-54
    DOI: 10.1287/deca.1110.0221
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    References listed on IDEAS

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    1. Jorge González-Ortega & Refik Soyer & David Ríos Insua & Fabrizio Ruggeri, 2021. "An Adversarial Risk Analysis Framework for Batch Acceptance Problems," Decision Analysis, INFORMS, vol. 18(1), pages 25-40, March.
    2. Jason R. W. Merrick & Fabrizio Ruggeri & Refik Soyer & L. Robin Keller, 2012. "From the Editors---Games and Decisions in Reliability and Risk," Decision Analysis, INFORMS, vol. 9(2), pages 81-85, June.
    3. Xiaojun (Gene) Shan & Jun Zhuang, 2014. "Modeling Credible Retaliation Threats in Deterring the Smuggling of Nuclear Weapons Using Partial Inspection---A Three-Stage Game," Decision Analysis, INFORMS, vol. 11(1), pages 43-62, March.
    4. Kaiyue Zheng & Laura A. Albert, 2019. "A Robust Approach for Mitigating Risks in Cyber Supply Chains," Risk Analysis, John Wiley & Sons, vol. 39(9), pages 2076-2092, September.
    5. Roponen, Juho & Ríos Insua, David & Salo, Ahti, 2020. "Adversarial risk analysis under partial information," European Journal of Operational Research, Elsevier, vol. 287(1), pages 306-316.
    6. L. Robin Keller, 2012. "From the Editor---Decisions over Time (Exploding Offers or Purchase Regret), in Game Settings (Embedded Nash Bargaining or Adversarial Games), and in Influence Diagrams," Decision Analysis, INFORMS, vol. 9(1), pages 1-5, March.
    7. Michael Macgregor Perry & Hadi El-Amine, 2021. "Computational Efficiency in Multivariate Adversarial Risk Analysis Models," Papers 2110.12572, arXiv.org.
    8. Hausken, Kjell, 2017. "Defense and attack for interdependent systems," European Journal of Operational Research, Elsevier, vol. 256(2), pages 582-591.
    9. Michael Perry & Hadi El-Amine, 2019. "Computational Efficiency in Multivariate Adversarial Risk Analysis Models," Decision Analysis, INFORMS, vol. 16(4), pages 314-332, December.
    10. Buede, Dennis M. & Mahoney, Suzanne & Ezell, Barry & Lathrop, John, 2012. "Using plural modeling for predicting decisions made by adaptive adversaries," Reliability Engineering and System Safety, Elsevier, vol. 108(C), pages 77-89.
    11. Michael Macgregor Perry, 2021. "Analyzing a Complex Game for the South China Sea Fishing Dispute using Response Surface Methodologies," Papers 2110.12568, arXiv.org, revised Dec 2021.
    12. Juan Luis Santos, 2014. "Application of adversarial risk testing to anomaly-based network intrusion detection systems," Journal of Socioeconomic Engineering, Instituto Universitario de Análisis Económico y Social, issue 2, pages 31-40, December.
    13. César Gil & David Rios Insua & Jesus Rios, 2016. "Adversarial Risk Analysis for Urban Security Resource Allocation," Risk Analysis, John Wiley & Sons, vol. 36(4), pages 727-741, April.
    14. William N. Caballero & Ethan Gharst & David Banks & Jeffery D. Weir, 2023. "Multipolar Security Cooperation Planning: A Multiobjective, Adversarial-Risk-Analysis Approach," Decision Analysis, INFORMS, vol. 20(1), pages 16-39, March.
    15. 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.
    16. Stefan Rass & Sandra König & Stefan Schauer, 2017. "Defending Against Advanced Persistent Threats Using Game-Theory," PLOS ONE, Public Library of Science, vol. 12(1), pages 1-43, January.
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    18. Mohammad E. Nikoofal & Mehmet Gümüs, 2015. "On the value of terrorist’s private information in a government’s defensive resource allocation problem," IISE Transactions, Taylor & Francis Journals, vol. 47(6), pages 533-555, June.

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