具有模糊支付的演化博弈策略研究
Research on Evolutionary Game Strategy with Fuzzy Payment
DOI: 10.12677/ecl.2024.1331042, PDF,    国家自然科学基金支持
作者: 鄢 迪, 丘小玲*：贵州大学数学与统计学院，贵州 贵阳
关键词: 演化博弈；模糊固定概率；混合更新过程；Evolutionary Game； Fuzzy Fixed Probability； Hybrid Renewal Process
摘要: 我们考虑个体基于Moran过程和模仿过程更新策略的过程，将两个过程结合起来建立混合随机演化博弈动力学。由于各种不确定性和复杂环境的影响，本文以模糊数的形式来给出了与环境因素相关的模糊博弈支付矩阵。首先，利用模糊数理论建立了具有模糊支付的混合更新随机演化博弈模型——Moran更新和模仿更新，并通过Fokker-Planck方程推导出不同模糊数下的模糊固定概率。其次，分析了模糊环境下混合更新演化博弈过程中策略占优的条件，得到模糊演化稳定策略；同时推导出弱选择下将博弈矩阵用梯形模糊数和正态模糊数表示时的模糊固定概率。最后，通过案例验证理论结果，并进行了仿真分析。
Abstract: We consider processes in which individuals update strategies based on Moran processes and imitative processes, and combine the two processes to establish hybrid stochastic evolutionary game dynamics. Due to the influence of various uncertainties and complex environments, this paper presents the fuzzy game payment matrix related to environment factors in the form of fuzzy numbers. Firstly, a hybrid update stochastic evolutionary game model with fuzzy payment, Moran update and imitation update, is established by fuzzy number theory, and the fuzzy fixed probabilities under different fuzzy numbers are derived by Fokker-Planck equation. Secondly, the conditions of strategy dominance in the mixed update evolutionary game under fuzzy environment are analyzed, and the fuzzy evolutionarily stable strategy is obtained. At the same time, the fuzzy fixed probability is derived when the game matrix is represented by trapezoidal fuzzy number and normal fuzzy number under weak selection. Finally, the theoretical results are verified by a case study, and the simulation analysis is carried out.
文章引用：鄢迪, 丘小玲. 具有模糊支付的演化博弈策略研究[J]. 电子商务评论, 2024, 13(3): 8504-8517. https://doi.org/10.12677/ecl.2024.1331042

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