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Bandwidth Scanning when the Rivals Are Subjective

  • Andrey GarnaevEmail author
  • Wade Trappe
Conference paper
Part of the Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering book series (LNICST, volume 277)

Abstract

In this paper we consider how subjectivity affects the problem of scanning spectrum bands, and the impact on both the scanner and invader’s strategy. To model such subjective behavior, we formulate a prospect theoretical (PT) extension of the Bayesian bandwidth scanning game where the Scanner knows only a priori probabilities about what type of intrusion (e.g. regular intensity or low intensity) occurs in the spectrum bands. Existence and uniqueness of the PT Bayesian equilibrium is proven. Moreover, these PT Bayesian equilibrium strategies are derived in closed form as functions of the detection probabilities associated with different invader types. Waterfilling equations are derived, which allows one to determine these detection probabilities. Bands where the Invader’s strategies have band-sharing form are identified. The sensitivity of the strategies to the subjective factors and a priori probabilities are numerically illustrated.

Keywords

Bayesian equilibrium Prospect theory Bandwidth scanning 

References

  1. 1.
    Altman, E., Avrachenkov, K., Garnaev, A.: Generalized \(\alpha \)-fair resource allocation in wireless networks. In: 47th IEEE Conference on Decision and Control (CDC 2008), Cancun, Mexico, pp. 2414–2419 (2009)Google Scholar
  2. 2.
    Anindya, I.C., Kantarcioglu, M.: Adversarial anomaly detection using centroid-based clustering. In: IEEE International Conference on Information Reuse and Integration (IRI), pp. 1–8 (2018)Google Scholar
  3. 3.
    Baston, V.J., Garnaev, A.Y.: A search game with a protector. Naval Res. Logistics 47, 85–96 (2000)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Comaniciu, C., Mandayam, N.B., Poor, H.V.: AWireless Networks Multiuser Detection in Cross-Layer Design. Springer, New York (2005)Google Scholar
  5. 5.
    Dambreville, F., Le Cadre, J.P.: Detection of a markovian target with optimization of the search efforts under generalized linear constraints. Naval Res. Logistics 49, 117–142 (2002)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Digham, F.F., Alouini, M.S., Simon, M.K.: On the energy detection of unknown signals over fading channels. IEEE Trans. Commun. 55, 21–24 (2007)CrossRefGoogle Scholar
  7. 7.
    Garnaev, A.: A remark on a helicopter and submarine game. Naval Res. Logistics 40, 745–753 (1993)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Garnaev, A., Garnaeva, G., Goutal, P.: On the infiltration game. Int. J. Game Theory 26, 215–221 (1997)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Garnaev, A., Trappe, W.: One-time spectrum coexistence in dynamic spectrum access when the secondary user may be malicious. IEEE Trans. Inf. Forensics Secur. 10, 1064–1075 (2015)CrossRefGoogle Scholar
  10. 10.
    Garnaev, A., Trappe, W.: A bandwidth monitoring strategy under uncertainty of the adversary’s activity. IEEE Trans. Inf. Forensics Secur. 11, 837–849 (2016)CrossRefGoogle Scholar
  11. 11.
    Garnaev, A., Trappe, W., Kung, C.-T.: Optimizing scanning strategies: selecting scanning bandwidth in adversarial RF environments. In: 8th International Conference on Cognitive Radio Oriented Wireless Networks (Crowncom), pp. 148–153 (2013)Google Scholar
  12. 12.
    Guan, S., Wang, J., Jiang, C., Tong, J., Ren, Y.: Intrusion detection for wireless sensor networks: a multi-criteria game approach. In: IEEE Wireless Communications and Networking Conference (WCNC), pp. 1–6 (2018)Google Scholar
  13. 13.
    Han, Z., Niyato, D., Saad, W., Basar, T., Hjrungnes, A.: Game Theory in Wireless and Communication Networks: Theory, Models, and Applications. Cambridge University Press, New York (2012)zbMATHGoogle Scholar
  14. 14.
    Hohzaki, R.: An inspection game with multiple inspectees. Eur. J. Oper. Res. 178, 894–906 (2007)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Hohzaki, R., Iida, K.: A search game with reward criterion. J. Oper. Res. Soc. Japan 41, 629–642 (1998)MathSciNetzbMATHGoogle Scholar
  16. 16.
    Jotshi, A., Batta, R.: Search for an immobile entity on a network. Eur. J. Oper. Res. 191, 347–359 (2008)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Kahneman, D., Tversky, A.: Prospect theory: an analysis of decision under risk. Econometrica 47, 263–291 (1979)CrossRefGoogle Scholar
  18. 18.
    Kahneman, D., Tversky, A.: Advances in prospect theory: cumulative representation of uncertainty. J. Risk Uncertainty 5, 297–323 (1992)CrossRefGoogle Scholar
  19. 19.
    Liu, S., Chen, Y., Trappe, W., Greenstein, L.J.: ALDO: an anomaly detection framework for dynamic spectrum access networks. In: IEEE International Conference on Computer (INFOCOM), pp. 675–683 (2009)Google Scholar
  20. 20.
    Poongothai, T., Jayarajan, K.: A noncooperative game approach for intrusion detection in mobile adhoc networks. In: International Conference on Computing, Communication and Networking, pp. 1–4 (2008)Google Scholar
  21. 21.
    Poor, H.V.: An Introduction to Signal Detection and Estimation. Springer, New York (1994).  https://doi.org/10.1007/978-1-4757-2341-0CrossRefzbMATHGoogle Scholar
  22. 22.
    Prelec, D.: The probability weighting function. Econometrica 90, 497–528 (1998)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Reddy, Y.B.: A game theory approach to detect malicious nodes in wireless sensor networks. In: Third International Conference on Sensor Technologies and Applications, pp. 462–468 (2009)Google Scholar
  24. 24.
    Saad, W., Sanjab, A., Wang, Y., Kamhoua, C.A., Kwiat, K.A.: Hardware trojan detection game: a prospect-theoretic approach. IEEE Trans. Veh. Technol. 66, 7697–7710 (2017)CrossRefGoogle Scholar
  25. 25.
    Sakaguchi, M.: Two-sided search games. J. Oper. Res. Soc. Japan 16, 207–225 (1973)MathSciNetzbMATHGoogle Scholar
  26. 26.
    Sanjab, A., Saad, W., Basar, T.: Prospect theory for enhanced cyber-physical security of drone delivery systems: a network interdiction game. In: IEEE International Conference on Communications (ICC), Paris, France (2017)Google Scholar
  27. 27.
    Sauder, D.W., Geraniotis, E.: Signal detection games with power constraints. IEEE Trans. Inf. Theory 40, 795–807 (1994)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Shen, S.: A game-theoretic approach for optimizing intrusion detection strategy in WSNs. In: 2nd International Conference on Artificial Intelligence, Management Science and Electronic Commerce (AIMSEC) (2011)Google Scholar
  29. 29.
    Vamvoudakis, K.G., Hespanha, J.P., Sinopoli, B., Mo, Y.: Adversarial detection as a zero-sum game. In: IEEE 51st IEEE Conference on Decision and Control (CDC), pp. 7133–7138 (2012)Google Scholar
  30. 30.
    Wang, X., Feng, R., Wu, Y., Che, S., Ren, Y.: A game theoretic malicious nodes detection model in MANETs. In: IEEE 9th International Conference on Mobile Ad-Hoc and Sensor Systems (MASS), pp. 1–6 (2012)Google Scholar
  31. 31.
    Xiao, L., Liu, J., Li, Q., Mandayam, N.B., Poor, H.V.: User-centric view of jamming games in cognitive radio networks. IEEE Trans. Inf. Forensics Secur. 10, 2578–2590 (2015)CrossRefGoogle Scholar
  32. 32.
    Xiao, L., Liu, J., Li, Y., Mandayam, N.B., Poor, H.V.: Prospect theoretic analysis of anti-jamming communications in cognitive radio networks. In: IEEE Global Communications Conference, pp. 746–751 (2014)Google Scholar
  33. 33.
    Xu, D., Xiao, L., Mandayam, N.B., Poor, H.V.: Cumulative prospect theoretic study of a cloud storage defense game against advanced persistent threats. In: IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS), pp. 541–546 (2017)Google Scholar

Copyright information

© ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering 2019

Authors and Affiliations

  1. 1.WINLABRutgers UniversityNorth BrunswickUSA

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