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Securing interdependent assets

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Abstract

Stackelberg security game models have become among the leading practical game theoretic approaches to security, having seen actual deployment in the LAX Airport, the United States Federal Air Marshals Service, and the United States Coast Guard, among others. However, most techniques for computing optimal security policies in Stackelberg games to date do not explicitly account for interdependencies among targets. We introduce a novel framework for computing optimal randomized security policies in networked (interdependent) domains. Our framework rests upon a Stackelberg security game model, within which we explicitly capture the indirect spread of damages due either to malicious attacks or unintended failures. We proceed to specify a particular simple, yet natural model of damage spread based on a graphical representation of asset interdependencies coupled with an independent failure cascade model. For the general model, we present an algorithm based on submodularity of the attacker’s decision problem, in combination with local search, to approximate optimal security resource allocation across the assets, and show experimentally that our algorithm is far more scalable than an alternative exact approach, yields nearly optimal results, and offers substantial improvement over a well-known heuristic alternative. We then show that in a particular important special case we can compute optimal security policies exactly and efficiently. We proceed to apply our framework to study comparative network resilience, unifying previously disparate strands of research in the area, and to offer insights into other aspects of the interdependent security problem.

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Notes

  1. The idea that the follower breaks ties in the leader’s favor may seem strange in the context of security games. However, note that the leader can make the follower strictly prefer the corresponding action by a slight change in his randomized policy.

  2. Note that it is direct to replace these choices by arbitrary different constants

  3. We assume here that both the defender and attacker share the same uncertainty about the network. An alternative model could consider an attacker that has more (or exact) information about the network. The resulting defender problem would become a Bayesian Stackelberg game.

  4. There are a plethora of minor variations on this general heuristic, but the performance of the best tends to be similar to this baseline.

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Acknowledgments

Much of this work was performed while Yevgeniy Vorobeychik was at Sandia National Laboratories and Joshua Letchford was at Duke University. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

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Authors and Affiliations

  1. Vanderbilt University, 2301 Vanderbilt Place, Nashville, TN, 37235-1679, USA

    Yevgeniy Vorobeychik

  2. Sandia National Laboratories, P.O. Box 969, Livermore, CA, USA

    Joshua Letchford

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  1. Yevgeniy Vorobeychik
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Correspondence to Yevgeniy Vorobeychik.

Additional information

Parts of this paper draw from the material previously presented at UAI 2012 [33]. Specifically, the model of interdependencies presented in [33] is a highly restricted special case of the model we present in this paper. Sects. 4.3, 6, and 7 draw upon [33], but much of the material in these sections is new.

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Vorobeychik, Y., Letchford, J. Securing interdependent assets. Auton Agent Multi-Agent Syst 29, 305–333 (2015). https://doi.org/10.1007/s10458-014-9258-0

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