[1]蔡江华,贾文生*,刘露萍.一类主从博弈Nash均衡点的存在性和稳定性[J].江西师范大学学报(自然科学版),2019,(03):277-281.[doi:10.16357/j.cnki.issn1000-5862.2019.03.10]
　CAI Jianghua,JIA Wensheng*,LIU Luping.The Existence and Stability of Nash Equilibrium Points for Single-Leader-Multi-Follower Games[J].Journal of Jiangxi Normal University:Natural Science Edition,2019,(03):277-281.[doi:10.16357/j.cnki.issn1000-5862.2019.03.10]
点击复制

一类主从博弈Nash均衡点的存在性和稳定性()
分享到：

《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2019年03期
页码:
277-281
栏目:
数学与应用数学
出版日期:
2019-06-10

文章信息/Info

Title:
The Existence and Stability of Nash Equilibrium Points for Single-Leader-Multi-Follower Games
文章编号:
1000-5862(2019)03-0277-05
作者:
蔡江华; 贾文生*; 刘露萍
贵州大学数学与统计学院,贵州 贵阳 550025
Author(s):
CAI Jianghua; JIA Wensheng*; LIU Luping
School of Mathematics and Statistics,Guizhou University,Guiyang Guizhou 550025,China
关键词:
主从博弈;  Nash均衡点;  伪连续;  本质连通区;  拟凹
Keywords:
leader-follower games;  Nash equilibrium points;  pseudo continuous;  essential component;  quasi concave
分类号:
O 225
DOI:
10.16357/j.cnki.issn1000-5862.2019.03.10
文献标志码:
A
摘要:
针对单个领导者与多个跟随者的主从博弈,在较弱的条件下,利用Berge极大值定理、Fan-Glicksberg不动点定理,证明了一类主从博弈Nash均衡点的存在性,推广和改进了已有的一些结果.在均衡点的稳定性方面,从最佳回应拓扑的角度证明了此类主从博弈存在Nash均衡点集的本质连通区.
Abstract:
Aiming at the leader-follower game between single leader and multiple followers,the existence of Nash equilibrium point for single-leader-multi-follower games is proved by using the Berge maximum theorem and the Fan-Glicksberg fixed point theorem under the weak condition,and some of the new results have promotion and improvement.In terms of the stability of equilibrium point,it is proved from the viewpoint of best response topology that the single-leader-multi-follower games have the essential components of the Nash equilibrium point sets.

参考文献/References:

[1] Stackelberg H V.The theory of the market economy[M].Oxford:Oxford University Press,1952:97-105.
[2] 梅生伟,魏韡.智能电网环境下主从博弈模型及应用实例[J].系统科学与数学,2014,34(11):1331-1344.
[3] 赵晗萍,蒋家东,冯允成.基于GA-RL的进化博弈求解主从博弈结构的供应链协调问题[J].系统工程理论与实践,2010,30(4):667-672.
[4] Julien L A.On noncooperative oligopoly equilibrium in the multiple leader-follower game[J].European Journal of Operational Research,2017,256(2):650-662.
[5] 俞建.博弈论选讲[M].北京:科学出版社,2014.
[6] 俞建.博弈论与非线性分析[M].北京:科学出版社,2008.
[7] 杨哲,蒲勇健.不确定性下多主从博弈中均衡的存在性[J].控制与决策,2012,27(5):736-740.
[8] 杨哲,蒲勇健.单主多从博弈中中级社会Nash均衡的存在性与应用[J].系统科学与数学,2013,33(7):777-784.
[9] 王晓,邬冬华.主从博弈的轻微利他平衡点[J].应用数学与计算数学学报,2015,29(4):479-485.
[10] 邓喜才,左羽.有限理性与一类多主从博弈问题的良定性[J].经济数学,2012,29(3):16-19.
[11] Yu Jian,Wang Honglei.An existence theorem of equilibrium points for multi-leader-follower games[J].Nonlinear Analysis,2008,69(5/6):1775-1777.
[12] Jia Wensheng,Xiang Shuwen,He Jihao,et al.Existence and stability of weakly Pareto-Nash equilibrium for generalized multi objective multi-leader-follower games[J].J Glob Optim,2015,61(2):397-405.
[13] Yang Zhe,Ju Yan.Existence and generic stability of cooperative equilibria for multi-leader-multi-follower games[J].J Glob Optim,2016,65(3):563-573.
[14] Zeng Jing,Zhang Wenyan.Existence and Levitin-Polyak well-posedness for a class of generalized multiobjective multi-leader-follower games[J].Pacific Journal of Optimization,2016,12(4):717-726.
[15] Pang Jongshi,Fukushima M.Quasi-variational inequalities,generalized Nash equilibria,and multi-leader-follower games[J].Comput Manag Sci,2005,2(1):21-56.
[16] 左勇华.约束形式下广义最大元Nash均衡的存在性[J].经济数学,2016,33(1):65-67.
[17] Morgan J,Scalzo V.Pseudocontinuous functions and existence of Nash equilibria[J].Journal of Mathematical Economics,2007,43(2):174-183.
[18] 俞建.有限理性与博弈论中平衡点集的稳定性[M].北京:科学出版社,2017.
[19] Aliprantis C D,Border K C.Infinite dimensional analysis[M].Berlin:Springer,1999.
[20] Yu Jian,Yang Hui,Xiang Shuwen.Unified approach to existence and stability of essential components[J].Nonlinear Analysis Theory Methods and Applications,2005,63(5):2415-2425.
[21] 俞建,陈国强,向淑文,等.本质连通区的存在性与稳定性[J].应用数学学报,2004,27(2):201-209.

相似文献/References:

[1]左勇华,卢美华.集族交运算的连续性和不动点、Fan Ky点的通有稳定性[J].江西师范大学学报(自然科学版),2016,40(01):39.
　ZUO Yonghua,LU Meihua.The Continuity of Sets' Intersection Operation and the Generic Stability of Fixed Point and Fan Ky Point[J].Journal of Jiangxi Normal University:Natural Science Edition,2016,40(03):39.

备注/Memo

备注/Memo:
收稿日期:2018-11-10
基金项目:国家自然科学基金(11561013),人社部留学归国人员择优(人社[2015]192),贵州省联合基金(黔科联合[2014]7643),贵州大学人才引进基金(贵大[2014]05)和贵州大学培育基金(黔科合平台人才[2017]5788)资助项目.
通信作者:贾文生(1981-),男,河南南阳人,副教授,博士,主要从事非线性分析与博弈论研究.E-mail:jws0505@163.com
更新日期/Last Update: 2019-06-10