Approximation Algorithm for Security Games with Costly Resources

  • Sayan Bhattacharya
  • Vincent Conitzer
  • Kamesh Munagala
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7090)


In recent years, algorithms for computing game-theoretic solutions have been developed for real-world security domains. These games are between a defender, who must allocate her resources to defend potential targets, and an attacker, who chooses a target to attack. Existing work has assumed the set of defender’s resources to be fixed. This assumption precludes the effective use of approximation algorithms, since a slight change in the defender’s allocation strategy can result in a massive change in her utility. In contrast, we consider a model where resources are obtained at a cost, initiating the study of the following optimization problem: Minimize the total cost of the purchased resources, given that every target has to be defended with at least a certain probability. We give an efficient logarithmic approximation algorithm for this problem.


Nash Equilibrium Approximation Algorithm Greedy Algorithm Approximation Ratio Costly Resource 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    An, B., Pita, J., Shieh, E., Tambe, M., Kiekintveld, C., Marecki, J.: GUARDS and PROTECT: next generation applications of security games. ACM SIGecom Exchanges 10(1), 31–34 (2011)CrossRefGoogle Scholar
  2. 2.
    Chen, X., Deng, X.: Settling the complexity of two-player Nash equilibrium. In: FOCS, pp. 261–272 (2006)Google Scholar
  3. 3.
    Daskalakis, C., Goldberg, P.W., Papadimitriou, C.H.: The complexity of computing a Nash equilibrium. In: STOC, pp. 71–78 (2006)Google Scholar
  4. 4.
    Dobson, G.: Worst-case analysis of greedy heuristics for integer programming with nonnegative data. Mathematics of Operations Research 7(4), 515–531 (1982)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Etessami, K., Yannakakis, M.: On the complexity of Nash equilibria and other fixed points. SIAM J. Comput. 39(6), 2531–2597 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Feige, U.: A threshold of ln n for approximating set-cover. Journal of the ACM 45(4), 634–652 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Hochbaum, D.: Approximation Algorithms for NP-hard Problems. PWS Publishing Company (1997)Google Scholar
  8. 8.
    Kiekintveld, C., Jain, M., Tsai, J., Pita, J., Ordóñez, F., Tambe, M.: Computing optimal randomized resource allocations for massive security games. In: AAMAS, pp. 689–696 (2009)Google Scholar
  9. 9.
    Korzhyk, D., Conitzer, V., Parr, R.: Complexity of computing optimal Stackelberg strategies in security resource allocation games. In: AAAI, pp. 805–810 (2010)Google Scholar
  10. 10.
    Nemhauser, G., Wolsey, L., Fisher, M.: An analysis of approximations for maximizing submodular set functions. Mathematical Programming 14(1), 265–294 (1978)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Pita, J., Jain, M., Ordóñez, F., Portway, C., Tambe, M., Western, C.: Using game theory for Los Angeles Airport security. AI Magazine 30(1), 43–57 (2009)CrossRefGoogle Scholar
  12. 12.
    Pita, J., Jain, M., Western, C., Portway, C., Tambe, M., Ordóñez, F., Kraus, S., Parachuri, P.: Deployed ARMOR protection: The application of a game-theoretic model for security at the Los Angeles International Airport. In: AAMAS - Industry and Applications Track, pp. 125–132 (2008)Google Scholar
  13. 13.
    Tsai, J., Rathi, S., Kiekintveld, C., Ordóñez, F., Tambe, M.: IRIS - a tool for strategic security allocation in transportation. In: AAMAS - Industry Track, pp. 37–44 (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Sayan Bhattacharya
    • 1
  • Vincent Conitzer
    • 1
  • Kamesh Munagala
    • 1
  1. 1.Department of Computer ScienceDuke UniversityDurhamUSA

Personalised recommendations