Skip to main content
SpringerLink
Log in

Risk Averse Stackelberg Security Games with Quantal Response

  • Conference paper
  • First Online:
Book cover Decision and Game Theory for Security (GameSec 2016)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9996))

Included in the following conference series:

Abstract

In this paper, we consider a Stackelberg security game (SSG) where a defender can simultaneously protect m out of n targets with \(n>m\) from an adversary that uses a quantal response (QR) to decide which target to attack. The main contribution consists in introducing risk aversion in the defender’s behavior by using an entropic risk measure. Our work extends the work in [20] to a model that considers a risk averse defender. In addition we improve the algorithms used in [20] by reducing the number of integer variables, outlining how this adapts to arbitrary linear constraints. Computational results are presented on large scale artificial instances, showing the qualitative advantages of using a risk measure rather than the expected value.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Camerer, C., Ho, T.-H., Chong, J.-K.: A cognitive hierarchy model of games. Q. J. Econ. 119(3), 861–898 (2004)

    Article  MATH  Google Scholar 

  2. CPLEX. V12. 1: User Manual for CPLEX (2009)

    Google Scholar 

  3. Dantzig, G.B.: Linear Programming and Extensions. Princeton University Press, Princeton (1963)

    Book  MATH  Google Scholar 

  4. Gilbert, E.: Gray codes and paths on the n-Cube. Bell Syst. Tech. J. 37(3), 815–826 (1958)

    Article  MathSciNet  Google Scholar 

  5. Haile, P., Hortaçsu, A., Kosenok, G.: On the empirical content of quantal response equilibrium. Am. Econ. Rev. 98(1), 180–200 (2008)

    Article  Google Scholar 

  6. HSL. A collection of fortran codes for large-scale scientific computation. http://www.hsl.rl.ac.uk/

  7. Kiekintveld, C., Jain, M., Tsai, J., Pita, J., Ordóñez, F., Tambe, M.: Computing optimal randomized resource allocations for massive security games. In: Proceedings of the 8th AAMAS Conference, Budapest, Hungary, vol. 1, pp. 689–696. International Foundation for AAMAS (2009)

    Google Scholar 

  8. Knuth, D.E.: The Art of Computer Programming: Sorting and Searching, vol. 3. Pearson Education, Upper Saddle River (1998)

    MATH  Google Scholar 

  9. McKelvey, R., Palfrey, T.: Quantal response equilibria for normal form games. Games Econ. Behav. 10(1), 6–38 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  10. Pirnay, H., Lopez-Negrete, R., Biegler, L.: Optimal sensitivity based on IPOPT. Math. Program. Comput. 4(4), 307–331 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  11. 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 AAMAS: Industrial Track, Cascais Miragem, Portugal, pp. 125–132. International Foundation for AAMAS (2008)

    Google Scholar 

  12. Pita, J., Jain, M., Ordóñez, F., Tambe, M., Kraus, S.: Solving stackelberg games in the real-world: addressing bounded rationality and limited observations in human preference models. Artif. Intell. J. 174(15), 1142–1171 (2010)

    Article  MATH  Google Scholar 

  13. Pratt, J.W.: Risk aversion in the small and in the large. Econometrica J. Econ. Soc. 32(1/2), 122–136 (1964)

    Article  MATH  Google Scholar 

  14. Stahl, D., Wilson, P.: Experimental evidence on players’ models of other players. J. Econ. Behav. Organ. 25(3), 309–327 (1994)

    Article  MATH  Google Scholar 

  15. Vielma, J.: Mixed integer linear programming formulation techniques. SIAM Rev. 57, 3–57 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  16. Von Stackelberg, H.: The Theory of the Market Economy. William Hodge, London (1952)

    Google Scholar 

  17. Wachter, A., Biegler, L.: On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming. Math. Program. 106(1), 25–57 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  18. Wright, J., Leyton-Brown, K., Beyond equilibrium: predicting human behavior in normal-form games. In: Proceedings of the 24th AAAI Conference on Artificial Intelligence, Atlanta, GA (2010)

    Google Scholar 

  19. Yang, R., Kiekintveld, C., Ordóñez, F., Tambe, M., John, R.: Improving resource allocation strategy against human adversaries in security games. In: 22th IJCAI Proceedings, Barcelona, Spain, vol. 22, pp. 458–464. AAAI Press (2011)

    Google Scholar 

  20. Yang, R., Ordóñez, F., Tambe, M.: Computing optimal strategy against quantal response in security games. In: Proceedings of the 11th AAMAS, Valencia, Spain, vol. 2, pp. 847–854. International Foundation for AAMAS (2012)

    Google Scholar 

Download references

Acknowledgments

Funded by Conicyt through grant FONDEF No. D10I1002.

Author information

Authors and Affiliations

  1. University of Colorado Denver, 1201 Larimer Street, Denver, CO, 80204, USA

    Renaud Chicoisne

  2. Universidad de Chile, Republica 701, Santiago, Chile

    Fernando Ordóñez

Authors
  1. Renaud Chicoisne
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fernando Ordóñez
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Renaud Chicoisne .

Editor information

Editors and Affiliations

  1. New York University , New York, New York, USA

    Quanyan Zhu

  2. The University of Melbourne , Melbourne, Victoria, Australia

    Tansu Alpcan

  3. University of Brighton , Brighton, United Kingdom

    Emmanouil Panaousis

  4. University of Southern California , Los Angeles, California, USA

    Milind Tambe

  5. Carnegie Mellon University , Pittsburgh, New York, USA

    William Casey

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing AG

About this paper

Cite this paper

Chicoisne, R., Ordóñez, F. (2016). Risk Averse Stackelberg Security Games with Quantal Response. In: Zhu, Q., Alpcan, T., Panaousis, E., Tambe, M., Casey, W. (eds) Decision and Game Theory for Security. GameSec 2016. Lecture Notes in Computer Science(), vol 9996. Springer, Cham. https://doi.org/10.1007/978-3-319-47413-7_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-47413-7_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-47412-0

  • Online ISBN: 978-3-319-47413-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation