带有环境反馈的不对称劳动分工博弈模型  

Game Model of Asymmetrical Division of Labor with Environmental Feedback

作　　者：袁海蕊 孟新柱 YUAN Hairui;MENG Xinzhu(College of Mathematics and Systems Science,Shandong University of Science and Technology,Qingdao,Shandong 266590,China)

机构地区：[1]山东科技大学数学与系统科学学院,山东青岛266590

出　　处：《数学建模及其应用》2021年第1期26-38,118,F0003,共15页Mathematical Modeling and Its Applications

基　　金：国家自然科学基金(11371230);山东省自然科学基金(ZR2019MA003);山东科技大学科研创新团队(2014TDJH102)。

摘　　要：带有环境反馈的两策略博弈被广泛研究,本文研究带有环境反馈的三策略博弈模型.环境被分为富裕斑块和贫穷斑块,富裕的斑块可以为玩家提供额外的环境收益,而贫穷斑块不为玩家提供任何收益.首先,建立模仿者动力学模型,推导模型平衡点稳定性的充分条件.该模型平衡点的稳定性取决于各策略的成本、富裕环境的收益、策略C对策略A和策略B的干扰以及策略A和策略B的合作效益.此外,通过对模型进行数值模拟,可以发现与初始期望结果一致,并且得到了在异质环境下各策略的频率.Many papers have extensively investigated two-strategy games with environmental feedback.In this paper,we investigate the three-strategy game model with environmental feedback.The environment is divided into rich patches and poor patches,the rich patch provides additional environmental benefits to the player and the poor patch provides nothing to the player.Firstly,we establish the simulated dynamics model and derive the sufficient conditions for the stability of the equilibrium point of the model.The stability of the equilibrium point of the model depends on the cost of each strategy,the benefit of the rich environment,the interference of strategy C to strategy A and B,and the cooperation benefit of strategy A and B.In addition,we perform numerical simulation on the model and find that it is consistent with the initial expected results,and obtain the frequencies of each strategy in the heterogeneous environment.

关 键 词：进化博弈论 异质环境 稳定性 模仿动力学 干扰 

分 类 号：O175[理学—数学]