有限理性下不确定性群体博弈弱NS平衡的稳定性  

Stability of Weak NS Equilibria for Population Games with Uncertain Parameters Under Bounded Rationality

作　　者：王明婷 杨光惠 杨辉 Wang Mingting;Yang Guanghui;Yang Hui(College of Mathematics and Statistics,Guizhou University,Guiyang 550025)

机构地区：[1]贵州大学数学与统计学院,贵阳550025

出　　处：《数学物理学报（A辑）》2022年第6期1812-1825,共14页Acta Mathematica Scientia

基　　金：国家自然科学基金项目(11271098);贵州省科技计划项目(黔科合基础[2019]1067号);贵州大学引进人才科研项目([2017]59);贵州省教学改革项目(201908)。

摘　　要：对不确定参数下群体博弈,基于策略调整过程中产生相应成本这一事实,该文提出了一种新的平衡——弱NS平衡,其思想是当给定不确定参数时,代理人因转变策略所获得的新增收益小于或等于其所增加的成本,并且在不确定参数的作用下都不会得到严格差的纯收益,因而代理人没有动力改变当前策略从而达到弱NS平衡.进一步,运用Kakutani不动点定理证明了弱NS平衡的存在性;其次,通过构造抽象的理性函数,建立相应的有限理性模型,证明了当纯收益函数发生扰动时,有限理性模型结构稳定进而对ϵ-弱NS平衡是鲁棒的.因此,在Baire分类意义下,有限理性框架下大多数不确定性群体博弈弱NS平衡是稳定的.最后通过算例验证了结果的正确性.For population games with uncertain parameters,a weak NS equilibrium is firstly proposed based on the fact that switching strategies cause corresponding costs.The underlying idea of a weak NS equilibrium is that the agents'new gained payoffs from strategy switch are less than or equal to the increased cost for a given uncertainty parameter;simultaneously,each population can not obtain strictly poor net profits under uncertain parameters,thus each agent in every population has no motivation to unilaterally change the current strategy and then they achieve a weak NS equilibrium.Secondly,the existence of weak NS equilibria is proven by Kakutani's fixed point theorem.Thirdly,by constructing an abstract rational function,a corresponding bounded rational model is established,and it is shown structural stability implying robustness.Therefore,the generic stability of weak NS equilibria for population games with uncertain parameters under bounded rationality is also obtained when the net profit function is perturbed.Finally,an example is illustrated the correctness of the above results.

关 键 词：群体博弈 弱NS平衡 有限理性 不确定性 结构稳定性 

分 类 号：O225[理学—运筹学与控制论]