具有模糊支付的混合更新演化博弈动态分析
Evolutionary Game Dynamics Analysis of Hybrid Updated Process with Fuzzy Payoffs
DOI: 10.12677/ecl.2024.1341325, 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: 模糊数；演化博弈；模糊固定概率；混合更新规则；Fuzzy Numbers； Evolutionary Game； Fuzzy Fixed Probability； Hybrid Update Rule
摘要: 文章利用模糊数来表征演化博弈中的不确定性，建立了具有模糊支付的混合更新随机演化博弈动力学系统。首先，利用模糊数的运算分析了模糊支付下的混合更新演化博弈过程，推导了基于混合更新规则下的模糊固定概率。其次，分析了成为模糊演化稳定策略的存在性条件，并得到弱选择下博弈支付以梯形模糊数、正态模糊数表示时的模糊固定概率。最后，利用具有模糊支付的混合更新演化博弈模型研究了矿工行为选择策略的博弈问题，并通过数值仿真分析了参数对模糊固定概率的影响，验证了理论结果。
Abstract: In this paper, the uncertainty in evolutionary game is characterized by fuzzy numbers, and a hybrid updated stochastic evolutionary game dynamic system with fuzzy payoffs is established. Firstly, the process of hybrid update evolutionary game under fuzzy payoffs is analyzed by fuzzy number operation, and the fuzzy fixed probability based on hybrid update rule is derived. Secondly, the existence condition of the fuzzy evolutionarily stable strategy is analyzed, and the fuzzy fixed probability is obtained when the game payoffs are represented by trapezoidal fuzzy number and normal fuzzy number under weak selection. Finally, the game problem of miners’ behavior selection strategy is studied by using hybrid updated evolutionary game model with fuzzy payoffs, and the influence of parameters on fuzzy fixed probability is analyzed by numerical simulation, and the theoretical results are verified.
文章引用：鄢迪, 丘小玲. 具有模糊支付的混合更新演化博弈动态分析[J]. 电子商务评论, 2024, 13(4): 1706-1716. https://doi.org/10.12677/ecl.2024.1341325

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