Making the Most of Our Regrets: Regret-Based Solutions to Handle Payoff Uncertainty and Elicitation in Green Security Games

  • Thanh H. Nguyen
  • Francesco M. Delle Fave
  • Debarun Kar
  • Aravind S. Lakshminarayanan
  • Amulya Yadav
  • Milind Tambe
  • Noa Agmon
  • Andrew J. Plumptre
  • Margaret Driciru
  • Fred Wanyama
  • Aggrey Rwetsiba
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9406)


Recent research on Green Security Games (GSG), i.e., security games for the protection of wildlife, forest and fisheries, relies on the promise of an abundance of available data in these domains to learn adversary behavioral models and determine game payoffs. This research suggests that adversary behavior models (capturing bounded rationality) can be learned from real-world data on where adversaries have attacked, and that game payoffs can be determined precisely from data on animal densities. However, previous work has, as yet, failed to demonstrate the usefulness of these behavioral models in capturing adversary behaviors based on real-world data in GSGs. Previous work has also been unable to address situations where available data is insufficient to accurately estimate behavioral models or to obtain the required precision in the payoff values.

In addressing these limitations, as our first contribution, this paper, for the first time, provides validation of the aforementioned adversary behavioral models based on real-world data from a wildlife park in Uganda. Our second contribution addresses situations where real-world data is not precise enough to determine exact payoffs in GSG, by providing the first algorithm to handle payoff uncertainty in the presence of adversary behavioral models. This algorithm is based on the notion of minimax regret. Furthermore, in scenarios where the data is not even sufficient to learn adversary behaviors, our third contribution is to provide a novel algorithm to address payoff uncertainty assuming a perfectly rational attacker (instead of relying on a behavioral model); this algorithm allows for a significant scaleup for large security games. Finally, to reduce the problems due to paucity of data, given mobile sensors such as Unmanned Aerial Vehicles (UAV), we introduce new payoff elicitation strategies to strategically reduce uncertainty.


Unman Aerial Vehicle Online Appendix Uncertainty Interval Piecewise Linear Approximation Animal Density 
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.



This research was supported by MURI Grant W911NF-11-1-0332 and by CREATE under grant number 2010-ST-061-RE0001. We wish to acknowledge the contribution of all the rangers and wardens in Queen Elizabeth National Park to the collection of law enforcement monitoring data in MIST and the support of Uganda Wildlife Authority, Wildlife Conservation Society and MacArthur Foundation, US State Department and USAID in supporting these data collection financially.


  1. 1.
    Basilico, N., Gatti, N., Amigoni, F.: Leader-follower strategies for robotic patrolling in environments with arbitrary topologies. In: AAMAS (2009)Google Scholar
  2. 2.
    Boutilier, C., Patrascu, R., Poupart, P., Schuurmans, D.: Constraint-based optimization and utility elicitation using the minimax decision criterion. Artif. Intell. 170, 686–713 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Braziunas, D., Boutilier, C.: Assessing regret-based preference elicitation with the utpref recommendation system. In: EC (2010)Google Scholar
  4. 4.
    Brown, M., Haskell, W.B., Tambe, M.: Addressing scalability and robustness in security games with multiple boundedly rational adversaries. In: GameSec (2014)Google Scholar
  5. 5.
    Brunswik, E.: The Conceptual Framework of Psychology. University of Chicago Press, New York (1952)Google Scholar
  6. 6.
    De Farias, D.P., Van Roy, B.: On constraint sampling in the linear programming approach to approximate dynamic programming. Math. Oper. Res. 29, 462–478 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Fang, F., Stone, P., Tambe, M.: When security games go green: designing defender strategies to prevent poaching and illegal fishing. In: IJCAI (2015)Google Scholar
  8. 8.
    French, S.: Decision Theory: An Introduction to the Mathematics of Rationality. Halsted Press, New York (1986)zbMATHGoogle Scholar
  9. 9.
    Haskell, W.B., Kar, D., Fang, F., Tambe, M., Cheung, S., Denicola, L.E.: Robust protection of fisheries with compass. In: IAAI (2014)Google Scholar
  10. 10.
    Kiekintveld, C., Islam, T., Kreinovich, V.: Security games with interval uncertainty. In: AAMAS (2013)Google Scholar
  11. 11.
    Kiekintveld, C., Jain, M., Tsai, J., Pita, J., Ordez, F., Tambe, M.: Computing optimal randomized resource allocations for massive security games. In: AAMAS (2009)Google Scholar
  12. 12.
    Korzhyk, D., Conitzer, V., Parr, R.: Complexity of computing optimal stackelberg strategies in security resource allocation games. In: AAAI (2010)Google Scholar
  13. 13.
    Letchford, J., Vorobeychik, Y.: Computing randomized security strategies in networked domains. In: AARM (2011)Google Scholar
  14. 14.
    McFadden, D.: Conditional logit analysis of qualitative choice behavior. Technical report (1972)Google Scholar
  15. 15.
    McKelvey, R., Palfrey, T.: Quantal response equilibria for normal form games. Game Econ. Behav. 10(1), 6–38 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Montesh, M.: Rhino poaching: a new form of organised crime1. University of South Africa, Technical report (2013)Google Scholar
  17. 17.
    Nguyen, T.H., Yadav, A., An, B., Tambe, M., Boutilier, C.: Regret-based optimization and preference elicitation for stackelberg security games with uncertainty. In: AAAI (2014)Google Scholar
  18. 18.
    Nguyen, T.H., Yang, R., Azaria, A., Kraus, S., Tambe, M.: Analyzing the effectiveness of adversary modeling in security games. In: AAAI (2013)Google Scholar
  19. 19.
    Nudelman, E., Wortman, J., Shoham, Y., Leyton-Brown, K.: Run the gamut: a comprehensive approach to evaluating game-theoretic algorithms. In: AAMAS (2004)Google Scholar
  20. 20.
    Pita, J., Jain, M., Tambe, O.M., Kraus, S., Magori-cohen, R.: Effective solutions for real-world stackelberg games: when agents must deal with human uncertainties. In: AAMAS (2009)Google Scholar
  21. 21.
    Qian, Y., Haskell, W.B., Jiang, A.X., Tambe, M.: Online planning for optimal protector strategies in resource conservation games. In: AAMAS (2014)Google Scholar
  22. 22.
    Secretariat, G.: Global tiger recovery program implementation plan: 2013–14. Report, The World Bank, Washington, DC (2013)Google Scholar
  23. 23.
    Shieh, E., An, B., Yang, R., Tambe, M., Baldwin, C., DiRenzo, J., Maule, B., Meyer, G.: Protect: a deployed game theoretic system to protect the ports of the united states. In: AAMAS (2012)Google Scholar
  24. 24.
    Tambe, M.: Security and Game Theory: Algorithms, Deployed Systems. Cambridge University Press, Lessons Learned (2011)CrossRefGoogle Scholar
  25. 25.
    Wilcox, R.: Applying Contemporary Statistical Techniques. Academic Press, New York (2002)Google Scholar
  26. 26.
    Wright, J.R., Leyton-Brown, K.: Level-0 meta-models for predicting human behavior in games. In: ACM-EC, pp. 857–874 (2014)Google Scholar
  27. 27.
    Yang, R., Ford, B., Tambe, M., Lemieux, A.: Adaptive resource allocation for wildlife protection against illegal poachers. In: AAMAS (2014)Google Scholar
  28. 28.
    Yang, R., Ordonez, F., Tambe, M.: Computing optimal strategy against quantal response in security games. In: AAMAS (2012)Google Scholar
  29. 29.
    Yin, Z., Jiang, A.X., Tambe, M., Kiekintveld, C., Leyton-Brown, K., Sandholm, T., Sullivan, J.P.: Trusts: scheduling randomized patrols for fare inspection in transit systems using game theory. AI Mag. 33, 59 (2012)Google Scholar
  30. 30.
    Yin, Z., Korzhyk, D., Kiekintveld, C., Conitzer, V., Tambe, M.: Stackelberg vs. nash in security games: Interchangeability, equivalence, and uniqueness. In: AAMAS (2010)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Thanh H. Nguyen
    • 1
  • Francesco M. Delle Fave
    • 1
  • Debarun Kar
    • 1
  • Aravind S. Lakshminarayanan
    • 2
  • Amulya Yadav
    • 1
  • Milind Tambe
    • 1
  • Noa Agmon
    • 3
  • Andrew J. Plumptre
    • 4
  • Margaret Driciru
    • 5
  • Fred Wanyama
    • 5
  • Aggrey Rwetsiba
    • 5
  1. 1.University of Southern CaliforniaLos AngelesUSA
  2. 2.Indian Institute of Technology MadrasChennaiIndia
  3. 3.Bar-Ilan UniversityRamat GanIsrael
  4. 4.Wildlife Conservation Society New YorkUSA
  5. 5.Uganda Wildlife AuthorityKampalaUganda

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