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庞漩 . 基于群智算法的无人机任务调度方法研究 [D ] . 哈尔滨 : 哈尔滨工业大学 , 2021 : 19 - 43 .

PANG X . Research on UAV task scheduling method based on swarm intelligence algorithm [D ] . Harbin : Harbin Institute of Technology , 2021 : 19 - 43 . (in Chinese)

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TANG J , LIU G , PAN Q T . A review on representative swarm intelligence algorithms for solving optimization problems applications and trends [J ] . IEEE-CAA Journal of Automatica Sinica , 2021 , 8 ( 10 ): 1627 - 1643 .

程传斌 , 倪艾辰 , 房翔宇 , 等 . 改进的动态A*-Q-Learning算法及其在无人机航迹规划中的应用 [J ] . 现代信息科技 , 2021 , 5 ( 9 ): 1 - 5 ,9.

CHENG C B , NI A C , FANG X Y , et al . Improved dynamic A*-Q-Learning algorithm and its application in UAV route planning [J ] . Modern Information Technology , 2021 , 5 ( 9 ): 1 - 5 ,9. (in Chinese)

轩书哲 , 柯良军 . 基于多智能体强化学习的无人机集群攻防对抗策略研究 [J ] . 无线电工程 , 2021 , 51 ( 5 ): 360 - 366 .

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CUI J J , LIU Y W , NALLANATHAN A . Multi-agent reinforcement learning-based resource allocation for UAV networks [J ] . IEEE Transactions on Wireless Communications , 2020 , 19 ( 2 ): 729 - 743 . DOI: 10.1109/TWC.7693 http://doi.org/10.1109/TWC.7693 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=7693 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=7693

朱立龙 , 荣俊美 , 张思意 . 政府奖惩机制下药品安全质量监管三方演化博弈及仿真分析 [J ] . 中国管理科学 , 2021 , 29 ( 11 ): 55 - 67 .

ZHU L L , RONG J M , ZHANG S Y . Three-party evolutionary game and simulation analysis of drug quality supervision under the government reward and punishment mechanism [J ] . Chinese Journal of Management Science , 2021 , 29 ( 11 ): 55 - 67 . (in Chinese)

郭本海 , 王涵 . 多方博弈情景下我国自主品牌轿车价值重构问题研究 [J ] . 中国管理科学 , 2018 , 26 ( 10 ): 140 - 151 .

GUO B H , WANG H . Study on the value reconstruction of own brand cars in China based on multi-player game [J ] . Chinese Journal of Management Science , 2018 , 26 ( 10 ): 140 - 151 . (in Chinese)

XIANG Y L , HANNA K . Intersexual resource competition and the evolution of sex-biased dispersal [J ] . Frontiers in Ecology and Evolution , 2019 , 7 : 111 . DOI: 10.3389/fevo.2019.00111 http://doi.org/10.3389/fevo.2019.00111 https://www.frontiersin.org/article/10.3389/fevo.2019.00111/full https://www.frontiersin.org/article/10.3389/fevo.2019.00111/full

WANG L , PAN F , LI Y J . Evolutionary game strategies analysis of economic development and environmental protection between local governments under central supervision mechanism in China [J ] . Sustainability , 2022 , 14 : 12498 - 12498 . DOI: 10.3390/su141912498 http://doi.org/10.3390/su141912498 https://www.mdpi.com/2071-1050/14/19/12498 https://www.mdpi.com/2071-1050/14/19/12498 The positive interaction between economic development and environmental protection is an important social issue which concerns people’s livelihoods. In order to explore the coordinated path of economic development and environmental protection, game models are constructed, successively, between local governments and among central-local governments by the evolutionary game method, and then, numerical simulation technology is used to analyze the results. The results show that the presented evolutionary stability strategies are consistent with the three stages of economic development and environmental protection since the reform and opening up in China. From the early to the middle stage, the sum of the special governance funds and local penalty fees play a key role; from the middle to the late stage, the heterogeneity coefficient between the local governments, local environmental governance costs, and environmental pollution losses plays a decisive role; during the late stage, the sum of the special governance funds and local penalty fees and the performance appraisal indicators play an important role. According to the above conclusions, local governments tend to choose environmental priority strategy, and the central government tends to choose a loose supervision strategy to achieve coordinated development by improving the phased planning for coordinated development, appropriately increasing the special governance funds and local penalty standards, and appropriately balancing the weights of the economic and environmental indicators.

高阳 , 田达 , 吴克钊 , 等 . 基于阈值公共品博弈的无人机集群干扰决策技术 [J ] . 无线电通信技术 , 2023 , 48 ( 6 ): 1034 - 1038 .

GAO Y , TIAN D , WU K Z , et al . UAV swarm jamming decision technique based on threshold public goods game model [J ] . Radio Communications Technology , 2023 , 48 ( 6 ): 1034 - 1038 . (in Chinese)

鞠锴 , 冒泽慧 , 姜斌 , 等 . 基于势博弈的异构多智能体系统任务分配和重分配 [J ] . 自动化学报 , 2023 , 48 ( 10 ): 2416 - 2428 .

JU K , MAO Z H , JIANG B , et al . Task allocation and reallocation for heterogeneous multiagent systems based on potential game [J ] . Acta Automatica Sinica , 2023 , 48 ( 10 ): 2416 - 2428 . (in Chinese)

彭雅兰 , 段海滨 , 魏晨 . 基于交替方向网络进化博弈的无人机集群任务分配 [J ] . 工程科学学报 , 2023 , 44 ( 4 ): 792 - 800 .

PENG Y L , DUAN H B , WEI C . UAV swarm task allocation algorithm based on the alternating direction method of multipliers network potential game theory [J ] . Chinese Journal of Engineering , 2023 , 44 ( 4 ): 792 - 800 . (in Chinese)

禹明刚 , 何明 , 张东戈 , 等 . 基于多元公共品演化博弈的无人作战集群策略占优条件 [J ] . 系统工程与电子技术 , 2021 , 43 ( 9 ): 2553 - 2561 . DOI: 10.12305/j.issn.1001-506X.2021.09.23 http://doi.org/10.12305/j.issn.1001-506X.2021.09.23 如何提高集群中合作者占比, 是无人集群作战中自主协同的关键问题之一。基于多元公共品演化博弈框架, 对无人作战集群策略占优条件进行了理论推导和特性分析。首先，给出无人集群自主协同需求, 建立基于愿景驱动的多元演化博弈模型。然后，以平均丰度函数为出发点, 理论推导多元演化博弈的合作策略占优条件。在此基础上, 针对线性和带门限值的两类公共品博弈, 仿真分析收益系数、愿景水平、门限值等参数对策略占优的影响, 获取两类博弈模型的策略占优特性。最后, 依据特性分析结果, 给出实现无人集群合作策略占优的建议, 为无人集群作战的机制设计提供决策支持。

YU M G , HE M , ZHANG D G , et al . Strategy dominance condition of unmanned combat cluster based on multi-player public goods evolutionary game [J ] . Systems Engineering and Electronics , 2021 , 43 ( 9 ): 2553 - 2561 . (in Chinese) DOI: 10.12305/j.issn.1001-506X.2021.09.23 http://doi.org/10.12305/j.issn.1001-506X.2021.09.23 How to improve the proportion of cooperators is one of the key problems of autonomous cooperation in unmanned cluster operations. This research makes theoretical derivation and characteristic analysis on the strategy dominance condition of unmanned combat cluster based on multi-player public goods evolutionary game. It starts with the requirement analysis of autonomous collaboration in unmanned cluster firstly. And the evolutionary game model of multi-player public goods based on aspiration-driven dynamics is established.Then, the average abundance function and strategy dominance condition are constructed by theoretical derivation. Furthermore, the influence of multiplication factor, threshold and aspiration level on the strategy dominance of linear public goods game and threshold public goods game are simulated. Finally, the rationalization proposals to improve the proportion of cooperators and achieve strategy dominance are suggested according to the simulation results, and to provide decision-making support for the mechanism design of unmanned cluster operation.

禹明刚 , 陈瑾 , 何明 , 等 . 基于演化博弈的社团网络无人集群协同机制 [J ] . 中国科学:技术科学 , 2023 , 53 ( 2 ): 221 - 242 .

YU M G , CHEN J , HE M , et al . Cooperative evolution mechanism of multiclustered unmanned swarm on community networks [J ] . Scientia Sinica Technological , 2023 , 53 ( 2 ): 221 - 242 . (in Chinese)

全吉 , 储育青 , 王先甲 . 具有惩罚策略的公共物品博弈与合作演化 [J ] . 系统工程理论与实践 , 2019 , 39 ( 1 ): 141 - 149 . DOI: 10.12011/1000-6788-2017-1059-09 http://doi.org/10.12011/1000-6788-2017-1059-09 采用演化博弈方法，研究具有代价的第二方惩罚机制对于公共物品博弈均衡选择及群体合作行为的影响.将群体策略选择过程描述成一个多维马氏过程，通过极限分布分析系统演化稳定状态.分别考虑只对背叛策略进行惩罚的一阶惩罚机制和同时对背叛及不惩罚背叛的合作（二阶背叛）都进行惩罚的二阶惩罚机制.研究发现，与一阶惩罚相比，二阶惩罚机制可以在更大参数范围内促进群体合作的产生，系统存在选择不同均衡结果的惩罚参数临界值.并将结果与复制动态模型进行了对比.

QUAN J , CHU Y Q , WANG X J . Public goods with punishment and the evolution of cooperation [J ] . Systems Engineering-Theory & Practice , 2019 , 39 ( 1 ): 141 - 149 . (in Chinese)

全吉 , 储育青 , 王先甲 . 自愿参与机制下的公共物品博弈与合作演化 [J ] . 系统工程学报 , 2020 , 35 ( 2 ): 188 - 200 .

QUAN J , CHU Y Q , WANG X J . Public goods game under voluntary participation mechanism and the evolution of cooperation [J ] . Journal of Systems Engineering , 2020 , 35 ( 2 ): 188 - 200 . (in Chinese)

张耀 . 公共品博弈中合作演化及异质性研究 [D ] . 杭州 : 杭州电子科技大学 , 2017 : 32 - 43 .

ZHANG Y . Evolutionary cooperation and heterogeneity in public goods game [D ] . Hangzhou : Hangzhou University of Electronic Science and Technology , 2017 : 32 - 43 . (in Chinese)

史冬梅 . 复杂网络上的合作涌现空间公共品博弈中的异质性研究 [D ] . 北京 : 中国科学技术大学 , 2011 : 47 - 73 .

SHI D M . Emergence of cooperation on the complex networks study on the inhomogeneity in spatial public goods games [D ] . Beijing : University of Science and Technology of China , 2011 : 47 - 73 . (in Chinese)

杨志虎 . 复杂网络上的演化博弈与合作演化动力学研究 [D ] . 西安 : 西安电子科技大学 , 2014 : 32 - 52 .

YANG Z H . Evolutionary games and evolutionary cooperation dynamics in complex networks [D ] . Xi’an : Xidian University , 2014 : 32 - 52 . (in Chinese)

胡灵慧 . 基于公共品博弈模型的复杂网络演化博弈动力学研究 [D ] . 成都 : 电子科技大学 , 2020 : 26 - 34 .

HU L H . Research on the game dynamics of complex network evolution based on public goods game [D ] . Chengdu : University of Electronic Science and Technology of China , 2020 : 26 - 34 . (in Chinese)

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LI X , TIAN X J . Research on SMEs’ reputation mechanism and default risk based on investors’ financial participation [J ] . Sustainability , 2022 , 14 ( 21 ): 14329 . DOI: 10.3390/su142114329 http://doi.org/10.3390/su142114329 https://www.mdpi.com/2071-1050/14/21/14329 https://www.mdpi.com/2071-1050/14/21/14329 Small and micro enterprises (SMEs) play a significant role in the market economy. While online lending has brought financial inclusion for SMEs’ borrowers, it has also increased the default risk, which restricts the normative development of online lending. To explore the impact of the reputation mechanism on borrowers’ default behavior, this paper provides a theoretical model of asymmetric information dynamic games under the online lending mechanism and an empirical study, which takes the number of bidders that reflects the investors’ participation as a proxy variable for the reputation effect factor. The theoretical model showed the borrowers’ default behavior is effectively restrained by the increase in the reputation effect factor in the reputation mechanism, and the empirical study found that an increase in the number of bidders can significantly reduce the risk of borrowers’ default, which verifies the conclusion of the theoretical model.

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XIE R , GU C F . A collaborative algorithm for European starling flocks [J ] . Journal of Wuhan University (Science Edition) , 2019 , 65 ( 3 ): 229 - 237 . (in Chinese)

张艳玲 , 刘爱志 , 孙长银 . 间接互惠与合作演化的若干问题研究进展 [J ] . 自动化学报 , 2018 , 44 ( 1 ): 1 - 12 .

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李阿明 , 王龙 . 时序网络控制 [J ] . 系统科学与数学 , 2019 , 39 ( 2 ): 184 - 202 . DOI: 10.12341/jssms13582 http://doi.org/10.12341/jssms13582 近年来, 网络科学的发展为探究复杂系统动力学提供了有效方法. 复杂网络控制的研究, 为我们通过外部输入控制系统状态的演化提供了新的思路. 针对时序网络控制这一新的研究方向, 文章首先介绍了其可控性方面相关研究现状. 其次, 文章梳理了在实现系统最优控制时所需考虑的控制能量及控制轨迹等相关研究结果. 最后总结了该领域仍需解决的重要问题并展望了未来研究方向.

LI A M , WANG L . Controlling temporal networks [J ] . Journal of Systems Science and Mathematical Sciences , 2019 , 39 ( 2 ): 184 - 202 . (in Chinese) DOI: 10.12341/jssms13582 http://doi.org/10.12341/jssms13582 In recent years, the development of network science offers an efficient way to explore various dynamics of complex systems. By virtue of the investigations on controlling complex networks, we can control the evolution of systems' states via admissible external inputs. In this paper, apart from reviewing explorations on the controllability of temporal networks, we present the recent progress on exploring the optimal control energy and control trajectory, which play a vital role in the implementation of control in practice. Finally, we discuss several open problems and possible research directions in this area.

王超 , 郭基联 , 符凌云 . 基于拓扑势的作战体系网络节点重要度评估方法 [J ] . 兵工学报 , 2020 , 41 ( 8 ): 1658 - 1664 . DOI: 10.3969/j.issn.1000-1093.2020.08.020 http://doi.org/10.3969/j.issn.1000-1093.2020.08.020 针对传统重要度排序算法无法客观全面评估作战体系中各装备实体重要度的不足，运用复杂网络理论，结合数学中的拓扑学和物理学中的场论思想，提出基于拓扑势的重要度排序方法。通过定义序列距离，引入覆盖率指标，对拓扑势排序结果与常规方法排序结果的相似度进行对比分析。设计一个作战想定示例，对基于拓扑势的重要度排序算法的有效性进行分析验证。结果表明，该算法可以精确客观地量化分析体系中不同装备对体系结构构建以及任务完成能力的支撑作用，为战时兵力部署、指挥体系构建、战场抢修决策提供重要依据。

WANG C , GUO J L , FU L Y . Research on evaluation method of node importance of combat system of systems network based on topological potential [J ] . Acta Armamentarii , 2020 , 41 ( 8 ): 1658 - 1664 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2020.08.020 http://doi.org/10.3969/j.issn.1000-1093.2020.08.020 The traditional importance ranking algorithm can not be used to objectively and comprehensively evaluate the importance of each equipment entity in the combat system-of-systems network. An importance ranking method based on topological potential is proposed based on complex network theory combining with the topology theory in mathematics and field theory in physics. A coverage index is introduced to compare and analyze the similarity between the topological potential ranking results and the conventional method ranking results by defing a sequenced distance. An operational scenario is designed to analyze and verify the effectiveness of the importance ranking algorithm based on topological potential. The results show that the proposed algorithm can accurately and objectively quantify the supporting roles of different equipment in the system-of-systems to the construction of the structure and the ability to complete the task, and provide an important basis for the wartime deployment of forces, the construction of command system-of-systems, and the battlefield repair decisions.

SHEN C , JUSUP M , SHI L , et al . Exit rights open complex pathways to cooperation [J ] . Journal of the Royal Society Interface , 2021 , 18 ( 174 ): 20200777 . DOI: 10.1098/rsif.2020.0777 http://doi.org/10.1098/rsif.2020.0777 https://royalsocietypublishing.org/doi/10.1098/rsif.2020.0777 https://royalsocietypublishing.org/doi/10.1098/rsif.2020.0777 We study the evolutionary dynamics of the Prisoner’s Dilemma game in which cooperators and defectors interact with another actor type called exiters. Rather than being exploited by defectors, exiters exit the game in favour of a small pay-off. We find that this simple extension of the game allows cooperation to flourish in well-mixed populations when iterations or reputation are added. In networked populations, however, the exit option is less conducive to cooperation. Instead, it enables the coexistence of cooperators, defectors, and exiters through cyclic dominance. Other outcomes are also possible as the exit pay-off increases or the network structure changes, including network-wide oscillations in actor abundances that may cause the extinction of exiters and the domination of defectors, although game parameters should favour exiting. The complex dynamics that emerges in the wake of a simple option to exit the game implies that nuances matter even if our analyses are restricted to incentives for rational behaviour.

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宫远强 , 张业鹏 , 马万鹏 , 等 . 无人机蜂群中的群体智能涌现机理 [J ] . 兵工学报 , 2023 , 44 ( 9 ): 2661 - 2671 . DOI: 10.12382/bgxb.2022.1181 http://doi.org/10.12382/bgxb.2022.1181 针对无人机蜂群中自主协同行为涌现机理难以解释的问题,提出一种多Agent系统中的自主协同行为涌现的分析方法,对系统的微观个体层、中观结构层和宏观网络层三个层面展开分析,自底向上地量化分析系统动态演化过程,揭示系统从微观到宏观的内在逻辑以及系统演变中的一些问题。通过计算实验方法构建无人机蜂群的计算实验模型,根据蜂群作战的关键特征设计无人机蜂群社团信息网络,引入公共物品博弈机制构建蜂群合作演化模型,并给出社团网络上蜂群的演化动力学过程。通过数值模拟,从无人机蜂群系统的不同层面量化分析蜂群协同行为的涌现现象,从而认识蜂群自主协同行为的涌现机理,并为无人机蜂群协同机制的优化提供决策支持。

GONG Y Q , ZHANG Y P , MA W P , et al . Mechanisms of group intelligence emergence in UAV swarms [J ] . Acta Armamentarii , 2023 , 44 ( 9 ): 2661 - 2671 . (in Chinese) DOI: 10.12382/bgxb.2022.1181 http://doi.org/10.12382/bgxb.2022.1181 Understanding the emergence of autonomous cooperative behavior in UAV swarms is a challenging problem. In this study, an analysis method for studying the autonomous cooperative behavior emergence in multi-agent systems is proposed. The method analyzes three levels of the system: the micro-individual layer, the meso-structure layer, and the macro-network layer. It also quantifies the dynamic evolution process of the system from the bottom up, revealing the internal logic of the system from micro to macro and identifying problems in system evolution. The computational experimental model of UAV swarms is also introduced, and the information network of UAV swarm association is designed according to the key features of swarm operations. The game mechanism for public goods is introduced, and the cooperative evolution model of swarms is constructed. The evolution dynamics of swarms on the association network is revealed. Through numerical simulation, the emergence of swarm cooperative behaviors is quantitatively analyzed from different levels of the UAV swarm system, so as to understand the emergence mechanisms of autonomous and cooperative swarm behaviors and provide decision support for the optimization of UAV swarm cooperative mechanisms.

王先甲 , 顾翠伶 , 赵金华 , 等 . 随机演化动态及其合作机制研究综述 [J ] . 系统科学与数学 , 2019 , 39 ( 10 ): 1533 - 1552 . DOI: 10.12341/jssms13701 http://doi.org/10.12341/jssms13701 演化博弈论为解释如何促进和维持合作的问题提供了强大理论框架. 对于有限种群, 随机性起着重要的作用, 可通过随机演化博弈动态来研究策略的演化. 基于随机过程的有限种群的演化博弈动态中, 不同的策略更新规则导致不同的演化博弈动态过程. 该文旨在对有限种群中基于随机过程的演化博弈动态及其合作机制的研究进行综述, 并分析未来发展趋势. 首先对不同策略更新规则下的演化动态研究进行综述,主要包括~Moran~过程、Wright-Fisher~过程、Fermi~过程及愿景更新过程, 然后对演化博弈理论框架下促合作机制进行综述, 最后分析探讨有限种群中随机演化博弈动态未来的研究.

WANG X J , GU C L , ZHAO J H , et al . A review of stochastic evolution dynamics and its cooperative mechanism [J ] . Journal of Systems Science and Mathematical Sciences , 2019 , 39 ( 10 ): 1533 - 1552 . (in Chinese) DOI: 10.12341/jssms13701 http://doi.org/10.12341/jssms13701 Evolutionary game theory provides a powerful theoretical framework for how unrelated and selfish individuals promote and sustain cooperation. Randomness plays an important role in finite population and the evolutionary dynamics can be studied through stochastic processes. In the evolutionary game dynamics of finite population based on stochastic process, different strategy updating rules lead to different evolutionary game dynamic processes. The purpose of this paper is to summarize the research status on the dynamics of evolutionary games and cooperation mechanism based on stochastic processes in finite populations, and to analyze its future development trend. Firstly, the research on evolutionary dynamics under different strategy updating rules is reviewed, including the Moran process, Wright-Fisher process, Fermi process and aspiration-driven updating process, and then the cooperation mechanism under the framework of evolutionary game theory is reviewed. Finally, the future research on stochastic evolutionary game dynamics of finite population is analyzed and discussed.

王刚 , 王志屹 , 张恩宁 , 等 . 多阶段平台动态防御的Markov演化博弈模型及迁移策略 [J ] . 兵工学报 , 2021 , 42 ( 8 ): 1690 - 1697 .

WANG G , WANG Z Y , ZHANG E N , et al . Markov evolutionary game model and migration strategies for multi-stage platform dynamic defense [J ] . Acta Armamentarii , 2021 , 42 ( 8 ): 1690 - 1697 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2021.08.013 http://doi.org/10.3969/j.issn.1000-1093.2021.08.013 Markov evolutionary game model and migration strategy of multi-stage platform dynamic defense are proposed to improve the efficiency of platform dynamic defense under persistent and periodic attacks. The cyclical and phased characteristics of platform dynamic defense are analyzed from the network attack and defense principle of platform dynamic defense, and the key parameters and revenue of multi-stage platform dynamic defense are calculated. Markov evolutionary game model of multi-stage platform dynamic defense is established. According to the stage of the game, the discount factor and transfer probability are introduced into the total revenue calculation. On this basis, the existence of Nash equilibrium in multi-stage Markov platform dynamic defense evolutionary game is studied, and the Nash equilibrium solution and optimal migration strategy selection algorithm are given. Finally, an example is given to design the analysis process of the migration strategy, and the effectiveness of the proposed model and migration strategy is verified by simulation.