Abstract：According to the complex correlation characteristics of the actual interdependent network and the important evaluation indicators in the network, five different coupling methods are proposed, and nine interdependent network models are established. Considering the information transmission, redistribution and cascading failures in the network, a cascading failure model based on betweenness artificial flow models is established. We based on the game theory, attack-defense game problems of critical infrastructure are analyzed from the perspective of complex network, and the robustness of various interdependent networks is analyzed. We discovered the preferences of game participants in the interdependent networks, providing decision support for the protection of infrastructure networks.
王淑良, 孙静雅, 卞嘉志, 张建华, 董琪琪, 李君婧. 基于博弈论的关联网络攻防博弈分析[J]. 复杂系统与复杂性科学, 2024, 21(2): 22-29.
WANG Shuliang, SUN Jingya, BIAN Jiazhi, ZHANG Jianhua, DONG Qiqi, LI Junjing. Attack-defense Game Analysis of Interdependent Networks Based on Game Theory[J]. Complex Systems and Complexity Science, 2024, 21(2): 22-29.
[1]ALCARAZ C, ZEADALLY S. Critical infrastructure protection: Requirements and challenges for the 21st century[J]. International journal of critical infrastructure protection, 2015, 8: 53-66. [2]卿斯汉.关键基础设施安全防护[J].信息网络安全,2015(2):1-6. QING S H. Security protection of critical infrastructure[J]. Netinfo Security, 2015 (2):1-6. [3]刘涛,陈忠,陈晓荣.复杂网络理论及其应用研究概述[J].系统工程,2005,23(6):1-7. LIU T, CHEN Z, CHEN X R. Overview of complex network theory and its application research [J]. Systems Engineering,2005,23(6):1-7. [4]郭鹏,杨晓琴.博弈论与纳什均衡[J].哈尔滨师范大学自然科学学报,2006,22(4):25-28. GUO P, YANG X Q. Game theory and Nash equilibrium [J]. Journal of Natural Sciences, Harbin Normal University, 2006,22 (4): 25-28. [5]周涛,柏文洁,汪秉宏,等.复杂网络研究概述[J].物理,2005,34(1):31-36. ZHOU T, BAI W J, WANG B H, et al. A brief review of complex networks[J]. Physics, 2005,34 (1): 31-36. [6]王哲,李建华,康东,等.复杂网络鲁棒性增强策略研究综述[J].复杂系统与复杂性科学,2020,17(3):1-26. Wang Z, LI J H,KANG D, et al. Review strategies enhance the robustness of complex network[J]. Complex Systems and Complexity Science, 2020,17(03):1-26. [7]RINALDI S M, PEERENBOOM J P, KELLY T K. Identifying, understanding, and analyzing critical infrastructure interdependencies[J]. IEEE Control Systems Magazine, 2001, 21(6): 11-25. [8]NOCHENSON A, HEIMANN C F L. Simulation and game-theoretic analysis of an attacker-defender game[C]//Decision and Game Theory for Security: Third International Conference, GameSec 2012, Budapest, Hungary, 2012: 138-151. [9]VESPIGNANI A. Complex networks: the fragility of interdependency[J]. Nature, 2010, 464:984-985. [10] 董政呈,方彦军,田猛.相互依存网络抗毁性研究综述[J].复杂系统与复杂性科学,2017,14(3):30-44. DONG Z C, FANG Y J, TIAN M, Review on vulnerability of interdependent networks[J]. Complex Systems and Complexity Science, 2017,14(3):30-44. [11] WU D, XIAO H, PENG R. Object defense with preventive strike and false targets[J]. Reliability Engineering & System Safety, 2018, 169: 76-80. [12] MACKENZIE C A, BAROUD H, BARKER K. Static and dynamic resource allocation models for recovery of interdependent systems: application to the Deepwater Horizon oil spill[J]. Annals of Operations Research, 2016, 236(1): 103-129. [13] WANG N, JIN Z Y, ZHAO J. Cascading failures of overload behaviors on interdependent networks[J]. Physica A: Statistical Mechanics and its Applications, 2021, 574: 125989. [14] 马海瑛,肖玉芝,赵海兴,等.三层复杂网络模型构建及特性分析[J].复杂系统与复杂性科学,2020,17(4):16-29. MA H Y, XIAO Y Z, ZHAO H X, et al. Three-Layer complex network model construction and characteristic analysis[J]. Complex Systems and Complexity Science, 2020,17(4):16-29. [15] HOTA A R, SUNDARAM S. Interdependent security games on networks under behavioral probability weighting[J]. IEEE Transactions on Control of Network Systems,2016,5(1): 262-273. [16] 徐云程,胡华,孙小军.三层无标度关联网络协同传播模型阈值研究[J].复杂系统与复杂性科学,2021,18(3):1-8. XU Y C, HU H, SUN X J, Research on threshold of cooperative propagation model of three-layer scale-free associative network[J]. Complex Systems and Complexity Science, 2021,18(3):1-8. [17] HAUSKEN K, LEVITIN G. Minmax defense strategy for complex multi-state systems[J]. Reliability Engineering & System Safety, 2009, 94(2): 577-587. [18] LI Y, LIN J, ZHANG C, et al. Joint optimization of structure and protection of interdependent infrastructure networks[J]. Reliability Engineering & System Safety, 2022, 218: 108163. [19] FU C Q, GAO Y J, ZHONG J L, et al. Attack-defense game for critical infrastructure considering the cascade effect[J]. Reliability Engineering & System Safety, 2021, 216: 107958. [20] PENG R, WU D, SUN M, et al. An attack-defense game on interdependent networks[J]. Journal of the Operational Research Society, 2021, 72(10): 2331-2341. [21] 任晓龙,吕琳媛.网络重要节点排序方法综述[J].科学通报,2014,59(13):1175-1197. REN X L, LÜ L Y. Review of ranking nodes in complex networks[J]. Chinese Science Bulletin, 2014,59(13):1175-1197. [22] 张强,曹军海,宋太亮,等.装备保障网络中考虑负载再分配的级联失效分析[J].兵器装备工程学报,2021,42(6):86-90. ZHANG Q, CAO J H,SONG T L, et al. Cascading failure analysis considering load redistribution in equipment support network[J]. Journal of Ordnance Equipment Engineering, 2021,42(6):86-90. [23] 种鹏云,尹惠.蓄意攻击策略下危险品运输网络级联失效仿真[J].复杂系统与复杂性科学,2018,15(1):45-55. ZHONG P Y, YIN H, Simulation of cascading failures on hazardous material transportation networks under targeted attack[J]. Complex Systems and Complexity Science, 2018,15(1):45-55. [24] OUYANG M. Comparisons of purely topological model, betweenness based model and direct current power flow model to analyze power grid vulnerability[J]. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2013, 23(2): 023114. [25] CRUCITTI P, LATORA V, MARCHIORI M. Model for cascading failures in complex networks[J]. Physical Review E, 2004, 69(4): 045104. [26] 王家辉.博弈论中的"囚徒困境"模型[J].统计与决策,2005(8):19-20. WANG J H. The "prisoner′s dilemma" model in game theory[J]. Statistics and Decision Making, 2005(8):19-20. [27] ZHANG C, RAMIREZ-MARQUEZ J E, WANG J. Critical infrastructure protection using secrecy-a discrete simultaneous game[J]. European Journal of Operational Research, 2015, 242(1): 212-221. [28] TARDOS E, VAZIRANI V V. Basic solution concepts and computational issues[DB/OL]. [2022-03-15] https://www.cs.cornell.edu/~eva/agtchap1.pdf. [29] LEMKE C E, HOWSON, J T J. Equilibrium points of bimatrix games[J]. Journal of the Society for Industrial and Applied Mathematics, 1964, 12(2): 413-423. [30] PORTER R, NUDELMAN E, SHOHAM Y. Simple search methods for finding a nash equilibrium[J]. Games and Economic Behavior, 2008, 63(2): 642-662. [31] NASH J F. Equilibrium points in n-person games[J]. Proceedings of the National Academy of Sciences, 1950, 36(1): 48-49.
