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Security Games with Ambiguous Information about Attacker Types

  • Youzhi Zhang
  • Xudong Luo
  • Wenjun Ma
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8272)

Abstract

There has been significant recent interest in security games, which are used to solve the problems of limited security resource allocation. In particular, the research focus is on the Bayesian Stackelberg game model with incomplete information about players’ types. However, in real life, the information in such a game is often not only incomplete but also ambiguous for lack of sufficient evidence, i.e., the defender could not precisely have the probability of each type of the attacker. To address this issue, we define a new kind of security games with ambiguous information about the attacker’s types. In this paper, we also propose an algorithm to find the optimal mixed strategy for the defender and analyse the computational complexity of the algorithm. Finally, we do lots of experiments to evaluate that our model.

Keywords

Mass Function Mixed Strategy Attack Type Stackelberg Game Focal Element 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Paruchuri, P., Pearce, J.P., Marecki, J., Tambe, M., Ordonez, F., Kraus, S.: Playing games for security: An efficient exact algorithm for solving Bayesian Stackelberg games. In: Proceedings of the 7th International Joint Conference on Autonomous Agents and Multiagent Systems, vol. 2, pp. 895–902 (2008)Google Scholar
  2. 2.
    Pita, J., Jain, M., Marecki, J., Ordóñez, F., Portway, C., Tambe, M., Western, C., Paruchuri, P., Kraus, S.: Deployed ARMOR protection: The application of a game theoretic model for security at the Los Angeles International Airport. In: Proceedings of the 7th International Joint Conference on Autonomous Agents and Multiagent Systems: Industrial Track, pp. 125–132 (2008)Google Scholar
  3. 3.
    Korzhyk, D., Yin, Z., Kiekintveld, C., Conitzer, V., Tambe, M.: Stackelberg vs. Nash in security games: An extended investigation of interchangeability, equivalence, and uniqueness. Journal of Artificial Intelligence Research 41(2), 297–327 (2011)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Tambe, M.: Security and game theory: Algorithms, deployed systems, lessons learned. Cambridge University Press, New York (2011)CrossRefGoogle Scholar
  5. 5.
    Yang, R., Kiekintveld, C., OrdóñEz, F., Tambe, M., John, R.: Improving resource allocation strategies against human adversaries in security games: An extended study. Artificial Intelligence 195, 440–469 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Ma, W., Luo, X., Liu, W.: An ambiguity aversion framework of security games under ambiguities. In: Proceedings of the 23rd International Joint Conference on Artificial Intelligence, pp. 271–278 (2013)Google Scholar
  7. 7.
    Zimmermann, E.: Globalization and terrorism. European Journal of Political Economy 27(suppl. 1), S152–S161 (2011)Google Scholar
  8. 8.
    Cronin, A.K.: Behind the curve: Globalization and international terrorism. International Security 27(3), 30–58 (2003)CrossRefGoogle Scholar
  9. 9.
    Shafer, G.: A mathematical theory of evidence. Princeton University Press, Princeton (1976)zbMATHGoogle Scholar
  10. 10.
    Liu, L., Yager, R.R.: Classic works of the Dempster-Shafer theory of belief functions: An introduction. In: Yager, R.R., Liu, L. (eds.) Classic Works of the Dempster-Shafer Theory of Belief Functions. Studies in Fuzziness and Soft Computing, vol. 219, pp. 1–34. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  11. 11.
    Strat, T.M.: Decision analysis using belief functions. International Journal of Approximate Reasoning 4(5), 391–417 (1990)CrossRefzbMATHGoogle Scholar
  12. 12.
    Ma, W., Xiong, W., Luo, X.: A model for decision making with missing, imprecise, and uncertain evaluations of multiple criteria. International Journal of Intelligent Systems 28(2), 152–184 (2013)CrossRefGoogle Scholar
  13. 13.
    Xiong, W., Luo, X., Ma, W.: Games with ambiguous payoffs and played by ambiguity and regret minimising players. In: Thielscher, M., Zhang, D. (eds.) AI 2012. LNCS, vol. 7691, pp. 409–420. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  14. 14.
    Dubois, D., Prade, H.: A note on measures of specificity for fuzzy sets. International Journal of General System 10(4), 279–283 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Jousselme, A.L., Liu, C., Grenier, D., Bosse, E.: Measuring ambiguity in the evidence theory. IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans 36(5), 890–903 (2006)CrossRefGoogle Scholar
  16. 16.
    Conitzer, V., Sandholm, T.: Computing the optimal strategy to commit to. In: Proceedings of the 7th ACM Conference on Electronic Commerce, pp. 82–90 (2006)Google Scholar
  17. 17.
    Smets, P., Kennes, R.: The transferable belief model. Artificial Intelligence 66(2), 191–234 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Eichberger, J., Kelsey, D.: Are the treasures of game theory ambiguous? Economic Theory 48(2-3), 313–339 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Marco, G.D., Romaniello, M.: Beliefs correspondences and equilibria in ambiguous games. International Journal of Intelligent Systems 27(2), 86–107 (2012)CrossRefGoogle Scholar
  20. 20.
    Wang, C., Tang, W., Zhao, R.: Static Bayesian games with finite fuzzy types and the existence of equilibrium. Information Sciences 178(24), 4688–4698 (2008)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Youzhi Zhang
    • 1
  • Xudong Luo
    • 1
  • Wenjun Ma
    • 2
  1. 1.Institute of Logic and CognitionSun Yat-sen UniversityGuangzhouChina
  2. 2.School of Electronics, Electrical Engineering and Computer ScienceQueen’s University BelfastBelfastUK

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