具有向量值支付的3级动态博弈模型及弱合作均衡的存在性  

Existence of Weak Cooperative Equilibrium in 3-Stage Dynamic Games with Vector Payoffs

作　　者：亢兵兵 管涛 李楠 宋奇庆 KANG Bing-bing;GUAN Tao;LI Nan;SONG Qi-qing(School of Mathematics and Computer Science,Shanxi Normal University,Taiyuan 030031,China)

机构地区：[1]山西师范大学数学与计算机科学学院,山西太原030031

出　　处：《数学的实践与认识》2025年第1期95-109,共15页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11661030);山西省回国留学人员科研资助项目(2024-086)。

摘　　要：将经典的效用型主从博弈扩展为向量值三阶段动态博弈,给出三阶段动态博弈的一般描述形式,建立向量值支付型的三阶段动态合作博弈模型,引入合作均衡的概念,对无限局中人的三阶段动态博弈定义一种弱合作均衡,研究均衡瓦解、合作均衡和弱合作均衡的特性,最后利用集值分析和拓扑方法,证明博弈的弱合作均衡的存在性.文章的模型和得到的结果扩展了主从博弈理论,研究表明新的模型并非原模型的简单推广,得到的结果包括了现有文献结果,也为未来多阶段主从博弈的合作均衡的研究提供了可能.This article extends the typical multi-leader-multi-follower games with utilities to a three-stage dynamic game and provides a general description of the three-stage dynamic game.It establishes a three-stage dynamic game model with vector payoffs,introduces the concept of cooperative equilibria,defines the concept of weak cooperative equilibria for games with infinite players,and studies the blocking of equilibria,the characteristics of cooperative equilibria and weak cooperative equilibria.Finally,by the set-valued analysis and topology,it proves the existence of weak cooperative equilibria.The model and the results extend the theory of dynamic games,and it is not the direct generalization of the original game.This includes the results in references,and provides the possibility for further research of cooperative equilibria in multi-stage multi-leader-multi-follower games.

关 键 词：主从博弈 3级动态博弈 向量值支付 弱合作均衡 α-核 

分 类 号：O225[理学—运筹学与控制论]