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Methods and Algorithms for Infinite Bayesian Stackelberg Security Games

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 6442))

Abstract

Recently there has been significant interest in applications of game-theoretic analysis to analyze security resource allocation decisions. Two examples of deployed systems based on this line of research are the ARMOR system in use at the Los Angeles International Airport [20], and the IRIS system used by the Federal Air Marshals Service [25]. Game analysis always begins by developing a model of the domain, often based on inputs from domain experts or historical data. These models inevitably contain significant uncertainty—especially in security domains where intelligence about adversary capabilities and preferences is very difficult to gather. In this work we focus on developing new models and algorithms that capture this uncertainty using continuous payoff distributions. These models are richer and more powerful than previous approaches that are limited to small finite Bayesian game models. We present the first algorithms for approximating equilibrium solutions in these games, and study these algorithms empirically. Our results show dramatic improvements over existing techniques, even in cases where there is very limited uncertainty about an adversaries’ payoffs.

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References

  1. Aghassi, M., Bertsimas, D.: Robust game theory. Mathematical Programming: Series A and B 107(1), 231–273 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  2. Agmon, N., Kraus, S., Kaminka, G.A., Sadov, V.: Adversarial uncertainty in multi-robot patrol. In: IJCAI (2009)

    Google Scholar 

  3. Alpcan, T., Basar, T.: A game theoretic approach to decision and analysis in network intrusion detection. In: Proc. of the 42nd IEEE Conference on Decision and Control, pp. 2595–2600 (2003)

    Google Scholar 

  4. Armantier, O., Florens, J.P., Richard, J.F.: Approximation of Bayesian Nash equilibrium. Journal of Applied Econometrics 23(7), 965–981 (2008)

    Article  MathSciNet  Google Scholar 

  5. Basiloco, N., Gatti, N., Amigoni, F.: Leader-follower strategies for robotic patrolling in environments with arbitrary topologies. In: AAMAS (2009)

    Google Scholar 

  6. Bier, V.M.: Choosing what to protect. Risk Analysis 27(3), 607–620 (2007)

    Article  Google Scholar 

  7. Cai, G., Wurman, P.R.: Monte Carlo approximation in incomplete information, sequential auction games. Decision Support Systems 39(2), 153–168 (2005)

    Article  Google Scholar 

  8. Ceppi, S., Gatti, N., Basilico, N.: Computing Bayes-Nash equilibria through support enumeration methods in Bayesian two-player strategic-form games. In: Proceedings of the ACM/IEEE International Conference on Intelligent Agent Technology (IAT), Milan, Italy, pp. 541–548 (September 15-18, 2009)

    Google Scholar 

  9. Conitzer, V., Sandholm, T.: Computing the optimal strategy to commit to. In: ACM EC, pp. 82–90 (2006)

    Google Scholar 

  10. Gatti, N.: Game theoretical insights in strategic patrolling: Model and algorithm in normal-form. In: ECAI, pp. 403–407 (2008)

    Google Scholar 

  11. Harsanyi, J.C.: Games with incomplete information played by Bayesian players (parts i–iii). Management Science 14 (1967-1968)

    Google Scholar 

  12. Kiekintveld, C., Jain, M., Tsai, J., Pita, J., Ordóñez, F., Tambe, M.: Computing optimal randomized resource allocations for massive security games. In: AAMAS (2009)

    Google Scholar 

  13. Kiekintveld, C., Marecki, J., Tambe, M.: Robust Bayesian methods for Stackelberg security games. In: Proceedings of the Ninth International Joint Conference on Autonomous Agents and Multi-agent systems (2010)

    Google Scholar 

  14. Krishna, V.: Auction Theory. Academic Press, London (2002)

    Google Scholar 

  15. Luce, R.D., Raiffa, H.: Games and Decisions. John Wiley and Sons, New York (1957); Dover republication (1989)

    MATH  Google Scholar 

  16. wei Lye, K., Wing, J.M.: Game strategies in network security. International Journal of Information Security 4(1-2), 71–86 (2005)

    Article  Google Scholar 

  17. McFadden, D.: Quantal choice analysis: A survey. Annals of Economic and Social Measurement 5(4), 363–390 (1976)

    Google Scholar 

  18. Nguyen, K.C., Basar, T.A.T.: Security games with incomplete information. In: Proc. of IEEE Intl. Conf. on Communications, ICC 2009 (2009)

    Google Scholar 

  19. Paruchuri, P., Pearce, J.P., Marecki, J., Tambe, M., Ordonez, F., Kraus, S.: Playing games with security: An efficient exact algorithm for Bayesian Stackelberg games. In: AAMAS, pp. 895–902 (2008)

    Google Scholar 

  20. Pita, J., Jain, M., Western, C., Portway, C., Tambe, M., Ordonez, F., Kraus, S., Paruchuri, P.: Depoloyed ARMOR protection: The application of a game-theoretic model for security at the Los Angeles International Airport. In: AAMAS (Industry Track) (2008)

    Google Scholar 

  21. Reeves, D.M., Wellman, M.P.: Computing best-response strategies in infinite games of incomplete information. In: UAI (2004)

    Google Scholar 

  22. Sandler, T., Daniel, G., Arce, M.: Terrorism and game theory. Simulation and Gaming 34(3), 319–337 (2003)

    Article  Google Scholar 

  23. von Stackelberg, H.: Marktform und Gleichgewicht. Springer, Vienna (1934)

    Google Scholar 

  24. Taylor, P., Jonker, L.: Evolutionary stable strategies and game dynamics. Mathematical Biosciences 16, 76–83 (1978)

    Google Scholar 

  25. Tsai, J., Rathi, S., Kiekintveld, C., Ordóñez, F., Tambe, M.: IRIS - A tools for strategic security allocation in transportation networks. In: AAMAS (Industry Track) (2009)

    Google Scholar 

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Kiekintveld, C., Marecki, J., Tambe, M. (2010). Methods and Algorithms for Infinite Bayesian Stackelberg Security Games. In: Alpcan, T., Buttyán, L., Baras, J.S. (eds) Decision and Game Theory for Security. GameSec 2010. Lecture Notes in Computer Science, vol 6442. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17197-0_18

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  • DOI: https://doi.org/10.1007/978-3-642-17197-0_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17196-3

  • Online ISBN: 978-3-642-17197-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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