B. Azibek, S. Kusdavletov, Aresh Dadlani, Quoc-Viet Pham, Behrouz Maham


Today, information security in defender-attacker game models is getting more attention from the research community. A game-theoretic approach applied in resource allocation study requires security in information for successive defensive strategy against attackers. For the defensive side players, allocating resources effectively and appropriately is essential to maintain the winning position against the attacking side. It can be possible by making the best response to the attack, i.e., by defining the most effective secure defensive strategy. This present work develops one defender – two attackers game model to determine the defensive strategy based on the Nash equilibrium and Stackelberg leadership equilibrium solutions of one defender-one attacker game model. Both game models are designed and studied in two scenarios: simultaneous and sequential modes. Game modes are defined according to the information that is available for attackers. In the first one, the defender is not aware of the attack and makes a simultaneous decision of how many resources should be allocated. Meanwhile, in the second mode, the defender knows about the entrance of attackers into a market and is assumed to commit a better strategy. The budget constraints are studied for both modes, all calculations and proof are presented in the work. According to obtained game mathematical models, it can be highlighted that network value of customers is important through the introduction of new variables in modeling and performing game theory equilibriums. This paper underlines the importance of information availability, budget limitations, and network value of customers in resource allocation through mathematical models and proofs; and focuses on modeling and studying defender-attacker games to define defensive strategy.

Ключевые слова

Game theory, defender-attackers model, one defender-two attackers model, resource allocation, social networks, Nash equilibrium, Stackelberg leadership model, optimal resource allocation, information security

Полный текст:



Deng, Z., & Kong, Z. (2020). Multi-Agent Cooperative Pursuit-Defense Strategy Against One

Single Attacker. IEEE Robotics And Automation Letters, 5(4), 5772-5778.


Fu, J., Li, Z., Sun, D., & Liu, W. (2013, November). Modeling multiple locations defence and attack

dynamic Bayesian decision game. In 2013 Sixth International Conference on Business Intelligence and

Financial Engineering (pp. 449-453). IEEE.

Friedman, L. (1958). Game-Theory Models in the Allocation of Advertising Expenditures. Operations

Research, 6(5), 699-709.

Ab Ghani, A. T., & Tanaka, K. (2011). Network Games with Many Attackers and Defenders. Proceedings

of Research Institute for Mathematical Sciences (RIMS) Kôkyûroku Kyoto University, 1729, 146-151.

Korzhyk, D., Conitzer, V., & Parr, R. (2011, June). Security games with multiple attacker resources.

In Twenty-Second International Joint Conference on Artificial Intelligence.

Lei, H., Huang, S., Liu, Y., & Zhang, T. (2019). Robust optimization for microgrid defense resource

planning and allocation against multi-period attacks. IEEE Transactions on Smart Grid, 10(5), 5841-

Li, Y., Xiao, L., Dai, H., & Poor, H. V. (2017, May). Game theoretic study of protecting MIMO transmissions

against smart attacks. In 2017 IEEE International Conference on Communications (ICC) (pp. 1-6). IEEE.

Masucci, A. M., & Silva, A. (2015, December). Defensive resource allocation in social networks.

In 2015 54th IEEE Conference on Decision and Control (CDC) (pp. 2927-2932). IEEE.

Sahabandu, D., Moothedath, S., Allen, J., Clark, A., Bushnell, L., Lee, W., & Poovendran, R. (2019,

December). Dynamic information flow tracking games for simultaneous detection of multiple

attackers. In 2019 IEEE 58th Conference on Decision and Control (CDC) (pp. 567-574). IEEE.

Sanjab, A., & Saad, W. (2016). Data injection attacks on smart grids with multiple adversaries:

A game-theoretic perspective. IEEE Transactions on Smart Grid, 7(4), 2038-2049. https://doi.


Vejandla, P., Dasgupta, D., Kaushal, A., & Nino, F. (2010, August). Evolving gaming strategies for

attacker-defender in a simulated network environment. In 2010 IEEE Second International Conference

on Social Computing (pp. 889-896). IEEE.

Wang, C., Hou, Y., & Ten, C. W. (2016). Determination of Nash equilibrium based on plausible attackdefense dynamics. IEEE Transactions on Power Systems, 32(5), 3670-3680.


Xiang, Y., & Wang, L. (2018). An improved defender–attacker–defender model for transmission line

defense considering offensive resource uncertainties. IEEE Transactions on Smart Grid, 10(3), 2534-

Xu, Z., & Zhuang, J. (2019). A study on a sequential one-defender-N-attacker game. Risk Analysis, 39(6),


Ye, M., & Hu, G. (2015). Distributed seeking of time-varying Nash equilibrium for non-cooperative

games. IEEE Transactions on Automatic Control, 60(11), 3000-3005.


Yuan, H., Xia, Y., Zhang, J., Yang, H., & Mahmoud, M. S. (2019). Stackelberg-game-based defense

analysis against advanced persistent threats on cloud control system. IEEE Transactions on Industrial

Informatics, 16(3), 1571-1580.

Zhang, J., & Zhuang, J. (2019). Modeling a multi-target attacker-defender game with multiple

attack types. Reliability Engineering & System Safety, 185, 465-475.


Zhang, J., Zhuang, J., & Jose, V. (2018). The role of risk preferences in a multi-target defenderattacker resource allocation game. Reliability Engineering & System Safety, 169, 95-104. https://doi.


Zhang, L., & Li, J. (2018). Enabling robust and privacy-preserving resource allocation in fog

computing. IEEE Access, 6, 50384-50393.

Zhang, X., Hipel, K. W., Ge, B., & Tan, Y. (2019). A game-theoretic model for resource allocation

with deception and defense efforts. Systems Engineering, 22(3), 282-291.


Zhang, X., Li, X., & Yuan, Z. (2019, October). Defending a single object in a defender-attacker game

considering time. In 2019 IEEE International Conference on Systems, Man and Cybernetics (SMC) (pp.

-510). IEEE.

Zhu, Q., Bushnell, L., & Başar, T. (2012, December). Game-theoretic analysis of node capture and

cloning attack with multiple attackers in wireless sensor networks. In 2012 IEEE 51st IEEE Conference

on Decision and Control (CDC) (pp. 3404-3411). IEEE.


  • Ссылки не определены.

(P): 2707-9031
(E): 2707-904X

Бизнес-центр EXPO, блок C.1.
Казахстан, 010000