引用本文:程乐峰,杨汝,王晓刚,余涛.三方多策略式博弈系统的长期演化稳定均衡特性研究[J].控制理论与应用,2021,38(10):1631~1661.[点击复制]
CHENG Le-feng,YANG Ru,WANG Xiao-gang,YU Tao.Investigation on long-term evolutionarily stable equilibrium characteristics of three-party multi-strategy game systems[J].Control Theory and Technology,2021,38(10):1631~1661.[点击复制]
三方多策略式博弈系统的长期演化稳定均衡特性研究
Investigation on long-term evolutionarily stable equilibrium characteristics of three-party multi-strategy game systems
摘要点击 3823  全文点击 717  投稿时间：2020-07-19  修订日期：2021-09-10
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DOI编号  10.7641/CTA.2021.00464
  2021,38(10):1631-1661
中文关键词  演化博弈论  三方多策略式演化博弈  长期演化稳定均衡  演化稳定策略  相对净支付  复制者动态
英文关键词  xevolutionary game theory  three-party multi-strategy evolutionary game  long-term evolutionarily stable equilibrium  evolutionarily stable strategy  relative net payoff  replicator dynamics
基金项目  广东省自然科学基金团队项目(1714060000016), 广东省教育厅创新强校工程项目(自科类)(2020KQNCX054), 广州大学人才培育项目(RP2021 017)资助.
作者单位E-mail
程乐峰 广州大学机械与电气工程学院 chenglefeng@gzhu.edu.cn 
杨汝* 广州大学机械与电气工程学院  
王晓刚 广州大学机械与电气工程学院  
余涛 华南理工大学电力学院  
中文摘要
      演化博弈论(EGT)基于有限理性假设且更加贴近现实, 近年来已在众多领域得到了初步应用. 基于此, 本文 关注一类较为常见的三方多策略式演化博弈系统, 尝试通过理论分析总结其长期演化稳定均衡(ESE)特性, 并进行 仿真验证研究. 首先, 研究了一般情形下的三方两策略对称与非对称演化博弈系统; 然后, 将其扩展到更复杂的三方 三策略非对称演化博弈类型, 并对其长期ESE特性进行了理论分析与动态仿真验证; 进一步, 对通用三方n-策略(n > 1)非对称演化博弈的建模思路进行了阐述与总结, 给出其收敛迭代的计算方法. 研究过程中详细定义了各类演化 博弈模型的相对净支付(RNP)参数. 实验结果表明可通过一些外部因素适当调整RNP参数使各类系统朝着期望的 长期ESE状态自发收敛. 最后, 进行了实例验证. 本文研究模型、方法和所得结论具有一定普适性, 旨在丰富EGT 研 究, 尤其是三方多策略演化博弈问题研究, 并为相关领域非完全理性人参与的行为决策问题研究提供一些思路和理 论参考.
英文摘要
      Based on assumption of bounded rationality, evolutionary game theory (EGT) is closer to reality compared with classical game theory. Focusing on general three-party multi-strategy evolutionary games, this paper attempts to summarize their long-term evolutionarily stable equilibrium (ESE) characteristics. Fristly, general three-party two-strategy symmetric and asymmetric evolutionary games are investigated. Then, the long-term ESE characteristics of more complex three-party three-strategy asymmetric games are theoretically analyzed and verified. Further, the modeling idea and convergence iteration method of general three-party n-strategy (n > 1) asymmetric evolutionary game are expounded and summarized. During the study, relative net payoff (RNP) parameters are defined for various evolutionary games. Research reveals that these games can spontaneously evolve toward an expected long-term ESE state by appropriately regulating their RNP parameters. Finally, the effectiveness of the proposed methods is verified. Overall, the research models, methods and conclusions have certain universality, aiming at enriching EGT research, especially for three-party multi-strategy evolutionary game issues, and providing some ideas for investigation of issues involving non-complete rational players.