摘要
本文在局中人的支付为模糊值函数的情况下,主要研究n人非合作模糊博弈和主从模糊博弈的Nash平衡存在性。首先,引入模糊数及它们之间的偏序关系、欧式空间Rn中连续模糊值函数及其保不等式性、最值性等性质。其次,建立模糊值函数对应的极大值定理。随后,利用这一极大值定理及Kakutani不动点定理证明了n人非合作模糊博弈Nash平衡的存在性。基于此,最后证明了主从模糊博弈Nash平衡存在性,并通过举例说明上述两类Nash平衡的存在性结果是有效的。
The existence of Nash equilibria of n-person non-cooperative fuzzy games and that of leader-follower fuzzy games are mainly studied in this paper,when the players’payoff functions are fuzzy value functions.Firstly,based on fuzzy number and its partial order relationship,a continuous fuzzy value function with its domain in Rn is introduced,and the properties such as inequality-preserving and maximum property are proved.Secondly,the maximum theorem under the fuzzy value function is established.Thirdly,the existence of Nash equilibria of n-person non-cooperative fuzzy games is proved by the maximum theorem and Kakutani fixed point theorem.Finally,based on above theorems,the existence of Nash equilibria of leader-follower fuzzy games is proved,and the validity of existence of Nash equilibria of the two fuzzy games is illustrated by examples.
作者
刘珍丽
王国玲
杨光惠
王明婷
LIU Zhen-li;WANG Guo-ling;YANG Guang-hui;WANG Ming-ting(School of Mathematics and Statistics,Guizhou University,Guiyang 550025,China)
出处
《模糊系统与数学》
北大核心
2023年第2期69-80,共12页
Fuzzy Systems and Mathematics
基金
国家自然科学基金资助项目(11271098)
贵州省科技计划项目(黔科合基础1067号)
贵州大学引进人才科研项目(59)
关键词
模糊值函数
极大值定理
n人非合作模糊博弈
主从模糊博弈
NASH平衡
Fuzzy Value Function
Maximum Theorem
n-person Non-cooperative Fuzzy Game
Leader-follower Fuzzy Game
Nash Equilibrium
作者简介
刘珍丽(1997-),女,研究方向:应用数学;王国玲(1992-),女,博士,研究方向:应用数学;通信作者:杨光惠(1976-),女,教授,研究方向:非合作博弈论,不确定性理论等;王明婷(1996-),女,研究方向:应用数学。
