Lexicographic programming for solving security game with fuzzy payoffs and computing optimal deception strategy

Document Type : Original Article

Authors

1 PhD, Student in Birjand University

2 Assistant Prof. in Birjand University

3 Assistant Prof , of Institute for the Study of War, Aja Command and Staff University,Tehran, I.R.Iran.

Abstract

Today, security and peace in different parts of society is one of the most important issues of mankind. Especially, due to the expansion of communications, the increase in international flights, and the development of transportation, the need to security is felt more than before. Achieving this requires predicting and preventing riots or attacks on various centers using scientific techniques. On the other hand, the limitations of security resources, including manpower and military facilities, have to be considered. Another challenge of security forces is that attackers observe the pattern of security forces before planning any attack. Therefore, defensive forces have to take into account the attacker's priorities in their decision making. Game theory provides a mathematical approach to utilize some limited security resources to maximize their efficiency. In this paper, a mathematical model is proposed to optimize the­­­ allocation of the forces, using a game theory analysis. Naturally, each player is unaware of the importance of targets for the other, exactly. In this model, in order to handle the players' uncertainty about the importance of targets, their payoffs are considered as triangular fuzzy numbers. Then, Lexicographic optimization is applied to solve the problem using an ordering relation on triangular fuzzy numbers. The final part of the paper deals with solving the security game problem with deceptive resources in the fuzzy environment in which, the defender can also use unrealistic resources to reduce the attacker's productivity, given the available budget.

Keywords

References

  • An, B. (2017, August). Game Theoretic Analysis of Security and Sustainability. In IJCAI (pp. 5111-5115).
  • An, B., Ordóñez, F., Tambe, M., Shieh, E., Yang, R., Baldwin, C., ... & Meyer, G. (2013). A deployed quantal response-based patrol planning system for the US Coast Guard. Interfaces, 43(5), 400-420.‏
  • Bigdeli, H., & Hassanpour, H. (2018). An approach to solve multi-objective linear production planning games with fuzzy parameters. Yugoslav Journal of Operations Research, 28(2), 237-248.‏
  •  Bigdeli, H., Hassanpour, H., & Tayyebi, J. (2017). Optimistic and Pessimistic Solutions of Single and Multi-Objective Matrix Games with Fuzzy Payoffs and Analysis of Some Military Cases.
  • Brown, G., Carlyle, M., Diehl, D., Kline, J., & Wood, K. (2005). A two-sided optimization for theater ballistic missile defense. Operations research, 53(5), 745-763.
  • Cohen, F., & Koike, D. (2004, June). Misleading attackers with deception. In Proceedings from the Fifth Annual IEEE SMC Information Assurance Workshop, 2004. (pp. 30-37). IEEE.‏
  • Conitzer, V., & Sandholm, T. (2006, June). Computing the optimal strategy to commit to. In Proceedings of the 7th ACM conference on Electronic commerce (pp. 82-90).‏
  • Ehrgott, M. (2005). Multicriteria optimization (Vol. 491). Springer Science & Business Media.‏
  • Ezzati, R., Khorram, E., & Enayati, R. (2015). A new algorithm to solve fully fuzzy linear programming problems using the MOLP problem. Applied mathematical modelling, 39(12), 3183-3193.
  • Fang, F., Nguyen, T. H., Pickles, R., Lam, W. Y., Clements, G. R., An, B., ... & Lemieux, A. (2016, February). Deploying PAWS: Field Optimization of the Protection Assistant for Wildlife Security. In AAAI (Vol. 16, pp. 3966-3973).
  • Jain, M., Kardes, E., Kiekintveld, C., Ordónez, F., & Tambe, M. (2010, July). Security games with arbitrary schedules: A branch and price approach. In AAAI.‏
  • Kiekintveld, C., Jain, M., Tsai, J., Pita, J., Ordóñez, F., & Tambe, M. (2009, May). Computing optimal randomized resource allocations for massive security games. In Proceedings of The 8th International Conference on Autonomous Agents and Multiagent Systems-Volume 1 (pp. 689-696).‏
  • Lye, K. W., & Wing, J. M. (2005). Game strategies in network security. International Journal of Information Security, 4(1-2), 71-86.‏
  • Paruchuri, P., Kraus, S., Pearce, J. P., Marecki, J., Tambe, M., & Ordonez, F. (2008). Playing games for security: An efficient exact algorithm for solving Bayesian Stackelberg games.‏
  • Pita, J., Jain, M., Marecki, J., Ordóñez, F., Portway, C., Tambe, M., ... & Kraus, S. (2008, May). Deployed ARMOR protection: the application of a game theoretic model for security at the Los Angeles International Airport. In Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems: industrial track (pp. 125-132).‏
  • Pita, J., Jain, M., Ordónez, F., Portway, C., Tambe, M., Western, C., ... & Kraus, S. (2009). Using game theory for Los Angeles airport security. AI magazine, 30(1), 43-43.‏
  • Sakawa, M. (2013). Fuzzy sets and interactive multiobjective optimization. Springer science & business media.‏
  • Sandler, T. & D. G. A. M. (2003). Terrorism and Game Theory, Simulation and Gaming, 34 (3): 319–337.
  • Tambe, M. (2011). Security and game theory: algorithms, deployed systems, lessons learned. Cambridge University Press.
  • Tambe, M., Jiang, A. X., An, B., & Jain, M. (2014, March). Computational game theory for security: Progress and challenges. In AAAI spring symposium on applied computational game theory.‏
  • Trejo, K. K., Clempner, J. B., & Poznyak, A. S. (2015). A Stackelberg security game with random strategies based on the extraproximal theoretic approach. Engineering Applications of Artificial Intelligence, 37, 145-153.

 Yin, Z., Korzhyk, D., Kiekintveld, C., Conitzer, V., & Tambe, M. (2010, May). Stackelberg vs. Nash in security games: Interchangeability, equivalence, and uniqueness. In Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1-Volume 1 (pp. 1139-1146).‏

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