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Network defense and behavioral biases: an experimental study

Abstract

How do people distribute defenses over a directed network attack graph, where they must defend a critical node? This question is of interest to computer scientists, information technology and security professionals. Decision-makers are often subject to behavioral biases that cause them to make sub-optimal defense decisions, which can prove especially costly if the critical node is an essential infrastructure. We posit that non-linear probability weighting is one bias that may lead to sub-optimal decision-making in this environment, and provide an experimental test. We find support for this conjecture, and also identify other empirically important forms of biases such as naive diversification and preferences over the spatial timing of the revelation of an overall successful defense. The latter preference is related to the concept of anticipatory feelings induced by the timing of the resolution of uncertainty.

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Notes

  1. 1.

    A non-exhaustive list of research considering the attack graph model from the Computer Security literature includes Sheyner and Wing (2003), Nguyen et al. (2010), Xie et al. (2010), Homer et al. (2013), and Hota et al. (2018). The length of this list and the ease in which it could be extended is indicative of the prominence that this literature places on the attack graph model.

  2. 2.

    A non-exhaustive list of related theory papers include Clark and Konrad (2007), Acemoglu et al. (2016), Dziubiński and Goyal (2013), Goyal and Vigier (2014), Dziubiński and Goyal (2017), Kovenock and Roberson (2018), and Bloch et al. (2020).

  3. 3.

    Sheremeta (2019) posits that things such as inequality aversion, spite, regret aversion, guilt aversion, loss aversion (see also Chowdhury, 2019), overconfidence and other emotional responses could all be important factors in (non-networked) attack and defense games. Preferences and biases have not received substantial attention in the experimental or theoretical literature in these games, although it should be noted that Chowdhury et al. (2013) and Kovenock et al. (2019) both find that utility curvature does not appear to be an important factor in multi-target attack and defense games.

  4. 4.

    See Kosfeld (2004) for a survey of network experiments more generally.

  5. 5.

    For example, Bier et al. (2007), Modelo-Howard et al. (2008), Dighe et al. (2009), An et al. (2013), Hota et al. (2016), Nithyanand et al. (2016), Guan et al. (2017), Wu et al. (2018), and Leibowitz et al. (2019).

  6. 6.

    The events are independent as each edge represents a unique layer of security that is unaffected by the events in other edges/layers of security. Breaches of other layers of security can affect whether a specific layer is encountered, but they do not change the probability that layer is compromised.

  7. 7.

    This approach is similar to the concept of ‘folding back’ sequential prospects, as described in Epper and Fehr-Duda (2018) with regards to ‘process dependence’. The alternative (i.e., \(f_j(x;\alpha )=w(p(x_1) +\left[ 1-p(x_1)\right] \left[ p(x_2) + (1-p(x_2))p(x_3) \right] )\)) does not yield interesting comparative statics in \(\alpha\) due to the monotonicity of the probability weighting function, so we do not consider it further.

  8. 8.

    Weighting the probability of a successful attack along an edge instead is analytically tractable as terms conveniently cancel, as shown in Abdallah et al. (2019b). However, this would be inconsistent with how events are ranked and weights are applied in RDU and CPT. Despite the lack of symmetry in the one parameter Prelec weighting function, the qualitative comparative statics presented in Abdallah et al. (2019b) have been numerically confirmed to hold in the current environment.

  9. 9.

    Concavity and diminishing marginal returns is a common assumption in the computer security literature (e.g., Pal and Golubchik 2010; Boche et al. 2011; Sun et al. 2018; Feng et al. forthcoming)

  10. 10.

    Any \(\alpha \in (0,1]\) defender is making a similar trade-off of \(\frac{\partial F(v,y)}{\partial v}\) against \(\frac{\partial F(v,y)}{\partial y}\), either equating them if the solution is interior, or allocating to whichever is greater at the boundary. We do not present these first order conditions here as they are not as succinct due to the presence of \(w(p;\alpha )\), although we do report the first order condition in Appendix A. Where exactly the trade-off is resolved depends on \(\alpha\) as well as the specific functional form of \(p(x_i)\). This is why the optimal allocation differs over \(\alpha\) for a given \(p(x_i)\), as well as over different \(p(x_i)\) for a given \(\alpha\). Both patterns are displayed in Figs. 2 and 3.

  11. 11.

    The normalization factor \(z=18.2\) was chosen such that 1 unit allocated to an edge would yield a commonly overweighted probability (\(p=0.05\)), while 24 units allocated to an edge would yield a commonly underweighted probability (\(p=0.73\)).

  12. 12.

    These numerical solutions are continuous, although subjects were restricted to discrete (integer-valued) allocations.

  13. 13.

    Further details are presented in Appendix A.

  14. 14.

    Another potential issue for both tasks is that subjects may not understand this point at all, instead of finding it simple. The number of such subjects should be limited due to our subject pool being drawn from a university student population.

  15. 15.

    In only 5 of the 4550 total decisions did subjects allocate less than all 24 units.

  16. 16.

    Due to an error with the software, decision times were not recorded for 4 subjects. For consistency, we present our results only considering the remaining 87 subjects. Where the inclusion of decision times is not necessary, our results do not substantially change if the dropped observations are included.

  17. 17.

    These instructions are available in Appendix G.

  18. 18.

    We consider the same analysis including the Binary Lottery Task in Appendix D. The elicited \(\alpha\)’s of these tasks are not correlated (\(\rho =0.166\), \(p=0.117\)), suggesting the procedural differences are important, or that cognitive ability may play a role.

  19. 19.

    Unless otherwise stated, all p-values and statistical tests are two-sided.

  20. 20.

    \(Prob(Top)=\frac{1}{1+e^{-\lambda (U(Top)-U(Bottom))}}\) if \(U(Top)\ge U(Bottom)\), \(Prob(Top)=\frac{1}{1+e^{-\lambda (U(Bottom)-U(Top))}}\) otherwise, where U(Top) is the weighted then compounded probability of successful attack multiplied by the payoff from a successful attack.

  21. 21.

    The lack of a significant correlation in Network Yellow is not necessarily surprising, due to the deliberate reduction of the separation of \(\alpha\) types in this network to evaluate Hypothesis 2.

  22. 22.

    We also cluster at the individual network task level in an alternative estimation presented in Appendix E. That analysis identifies similar patterns of behavior.

  23. 23.

    It is of course possible that subjects are playing out the attack process in their imagination, while reading the outcomes sequentially.

  24. 24.

    Choi et al. (2018) reports evidence suggesting a correlation between cognitive ability and probability weighting.

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This research was supported by grant CNS-1718637 from the National Science Foundation. We thank the editor, two anonymous referees, and participants at the Economic Science Association and Jordan-Wabash conferences for valuable comments.

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Woods, D., Abdallah, M., Bagchi, S. et al. Network defense and behavioral biases: an experimental study. Exp Econ (2021). https://doi.org/10.1007/s10683-021-09714-x

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Keywords

  • Laboratory experiment
  • Probability weighting
  • Naive diversification
  • Network security