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Game-Theoretic Goal Recognition Models with Applications to Security Domains

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Decision and Game Theory for Security (GameSec 2017)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10575))

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Abstract

Motivated by the goal recognition (GR) and goal recognition design (GRD) problems in the artificial intelligence (AI) planning domain, we introduce and study two natural variants of the GR and GRD problems with strategic agents, respectively. More specifically, we consider game-theoretic (GT) scenarios where a malicious adversary aims to damage some target in an (physical or virtual) environment monitored by a defender. The adversary must take a sequence of actions in order to attack the intended target. In the GTGR and GTGRD settings, the defender attempts to identify the adversary’s intended target while observing the adversary’s available actions so that he/she can strengthens the target’s defense against the attack. In addition, in the GTGRD setting, the defender can alter the environment (e.g., adding roadblocks) in order to better distinguish the goal/target of the adversary.

We propose to model GTGR and GTGRD settings as zero-sum stochastic games with incomplete information about the adversary’s intended target. The games are played on graphs where vertices represents states and edges are adversary’s actions. For the GTGR setting, we show that if the defender is restricted to playing only stationary strategies, the problem of computing optimal strategies (for both defender and adversary) can be formulated and represented compactly as a linear program. For the GTGRD setting, where the defender can choose K edges to block at the start of the game, we formulate the problem of computing optimal strategies as a mixed integer program, and present a heuristic algorithm based on LP duality and greedy methods. Experiments show that our heuristic algorithm achieves good performance (i.e., close to defender’s optimal value) with better scalability compared to the mixed-integer programming approach.

In contrast with our research, existing work, especially on GRD problems, has focused almost exclusively on decision-theoretic paradigms, where the adversary chooses its actions without taking into account the fact that they may be observed by the defender. As such an assumption is unrealistic in GT scenarios, our proposed models and algorithms fill a significant gap in the literature.

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Notes

  1. 1.

    Another perspective: from the previous section we see that \(\lambda ^\theta _{s,j}\) is the probability that adversary type \(\theta \) traverses the edge s, j. Then if the adversary and defender do not change their strategies after the edge (s, j) is blocked, the defender would receive an additional utility of \(M\sum _{\theta \in B} \lambda ^\theta _{s,j}\) from the adversary’s penalty for crossing that edge.

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Authors and Affiliations

  1. Department of Computer Science, Trinity University, San Antonio, TX, 78212, USA

    Samuel Ang & Albert Xin Jiang

  2. Department of Computer Science and Engineering, University of Nebraska-Lincoln, Lincoln, NE, 68588, USA

    Hau Chan

  3. Department of Computer Science and Engineering, Washington University in St. Louis, St. Louis, MO, 63130, USA

    William Yeoh

Authors
  1. Samuel Ang
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  2. Hau Chan
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  3. Albert Xin Jiang
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  4. William Yeoh
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Corresponding author

Correspondence to Samuel Ang .

Editor information

Editors and Affiliations

  1. Universität Klagenfurt, Klagenfurt, Austria

    Stefan Rass

  2. Nanyang Technological University, Singapore, Singapore

    Bo An

  3. University of Texas at El Paso, El Paso, Texas, USA

    Christopher Kiekintveld

  4. Carnegie Mellon University, Pittsburgh, Pennsylvania, USA

    Fei Fang

  5. AIT Austrian Institute of Technology GmbH, Klagenfurt, Austria

    Stefan Schauer

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Ang, S., Chan, H., Jiang, A.X., Yeoh, W. (2017). Game-Theoretic Goal Recognition Models with Applications to Security Domains. In: Rass, S., An, B., Kiekintveld, C., Fang, F., Schauer, S. (eds) Decision and Game Theory for Security. GameSec 2017. Lecture Notes in Computer Science(), vol 10575. Springer, Cham. https://doi.org/10.1007/978-3-319-68711-7_14

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  • DOI: https://doi.org/10.1007/978-3-319-68711-7_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-68710-0

  • Online ISBN: 978-3-319-68711-7

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