海上基地攻防博弈模型及纳什均衡策略研究

doi:10.12305/j.issn.1001-506X.2022.08.22

系统工程与电子技术 ›› 2022, Vol. 44 ›› Issue (8): 2570-2580.doi: 10.12305/j.issn.1001-506X.2022.08.22

海上基地攻防博弈模型及纳什均衡策略研究

曾斌¹, 王睿^2,*, 李厚朴³, 张鸿强¹

1. 海军工程大学管理工程与装备经济系, 湖北武汉 430033
2. 海军工程大学教研保障中心, 湖北武汉 430033
3. 海军工程大学导航工程系, 湖北武汉 430033

收稿日期:2021-05-26 出版日期:2022-08-01 发布日期:2022-08-24
通讯作者: 王睿
作者简介:曾斌(1970—), 男, 教授, 博士, 主要研究方向为信息管理|王睿(1975—), 女, 硕士, 主要研究方向为信息管理|李厚朴(1985—), 男, 教授, 博士, 主要研究方向为计算机代数分析|张鸿强(1996—), 男, 硕士研究生, 主要研究方向为信息管理
基金资助:
国家自然科学基金(41771487);湖北省杰出青年科学基金(2019CFA086)

Nash equilibrium strategy and attack-defense game model for naval support base

Bin ZENG¹, Rui WANG^2,*, Houpu LI³, Hongqiang ZHANG¹

1. Department of Management and Economics, Naval University of Engineering, Wuhan 430033, China
2. Teaching and Research Support Center, Naval University of Engineering, Wuhan 430033, China
3. Department of Navigation Engineering, Naval University of Engineering, Wuhan 430033, China

Received:2021-05-26 Online:2022-08-01 Published:2022-08-24
Contact: Rui WANG

摘要/Abstract

摘要：

针对海上保障基地安全的反潜资源调度是当前海上作战指挥的主要问题，通过分析海上利益冲突中敌我双方的攻防策略及约束条件, 建立了反潜资源调度的不完全信息零和博弈模型和对应的收益矩阵。考虑敌方为理性对手和非理性对手2种情况, 分别提出了求解小规模问题精确解的线性规划算法和求解大规模近似解的改进迭代算法, 并进一步给出了对应纳什均衡和最优反应的求解步骤, 得到了反潜资源调度博弈的混合策略。通过仿真实验验证了算法的复杂性、可行性和有效性, 并分析了混合策略的适用环境。

关键词: 保障基地, 反潜作战, 机器博弈, 纳什均衡

Abstract:

It is the key problem for naval command and control to schedule the anti-submarine teams between naval support bases. A zero sum game model with imperfect information and corresponding payoff matrix for the anti-submarine scheduling is designed through the analysis of attack and defense strategies with constraints of both sides in maritime conflict of interest. The linear programming algorithms for exact solution of small-scale problems and the improved iteration algorithms for approximate solution of large-scale problems are respectively proposed to consider the hostile forces are rational opponents and irrational opponents. The mixed strategy of anti-submarine scheduling can be obtained through the proposed computation procedure of Nash equilibrium and best response. The simulation results verified the complexity, feasibility and effectiveness of the algorithms and the application environment of the mixed strategy is analyzed.

Key words: support base, anti-submarine warfare, computer game, Nash equilibrium

中图分类号:

TN948.16

曾斌, 王睿, 李厚朴, 张鸿强. 海上基地攻防博弈模型及纳什均衡策略研究[J]. 系统工程与电子技术, 2022, 44(8): 2570-2580.

Bin ZENG, Rui WANG, Houpu LI, Hongqiang ZHANG. Nash equilibrium strategy and attack-defense game model for naval support base[J]. Systems Engineering and Electronics, 2022, 44(8): 2570-2580.

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算法	相对利用率	相对被利用率
NLP	0	0
BRLP	1.59	0.14
RMCFR	0.73	0.73
UUCFR	1.48	2.8

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海上基地攻防博弈模型及纳什均衡策略研究

Nash equilibrium strategy and attack-defense game model for naval support base

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