基于局中人偏好的主从博弈α-核与弱α-核的存在性  

Existence ofα-Core and Weakα-Core for Multi-Leader-Multi-Follower Games with Preferences

作　　者：仝佳琦 宋宛玲 宋奇庆 TONG Jiaqi;SONG Wanling;SONG Qiqing(School of Mathematics and Computer Science,Shanxi Normal University,Taiyuan 030031)

机构地区：[1]山西师范大学数学与计算机科学学院,太原030031

出　　处：《系统科学与数学》2024年第8期2350-2364,共15页Journal of Systems Science and Mathematical Sciences

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)资助课题。

摘　　要：文章给出了局中人具有偏好的主从博弈模型,提出了具有偏好的主从博弈的α-核的概念,并证明了该模型中α-核的存在性,Yang和Ju(2016)在效用表示下的主从博弈合作解的存在性结果扩展到了具有一般偏好的主从博弈模型,从而拓展了主从博弈的种类,给出了主从博弈合作解的更一般的描述形式,进而可以包括一些连续与非连续效用型的主从博弈模型,又通过定义局部FS-majorized条件,证明了具有更广义的偏好的主从博弈的α-核的存在性.进一步,文章给出了当主从博弈模型中有无限局中人时,具有偏好的主从博弈弱α-核的概念,并对其存在性进行了深入研究,最后证明了主从博弈的弱α-核的存在性.In this paper,we introduce the model of multi-leader-multi-follower games with preferences,propose the concept of theα-core of multi-leader-multi-follower games with preferences,and prove the existence ofα-core in this model.This generalizes Yang and Ju's(2016)results under the utility representation to the multi-leadermulti-follower games model with general preferences.Thus,it expands the kinds of multi-leader-multi-follower games and gives a more general description of cooperative solutions of multi-leader-multi-follower games.Furthermore,it can include some continuous and non-continuous utility type multi-leader-multi-follower game models.Using the locally FS-majorized conditions,this paper proves the existence ofα-core of multi-leader-multi-follower games with preferences.Further,this paper gives the concept of weakα-core of multi-leader-multi-follower games with general preferences when the multi-leader-multi-follower games have infinite leaders and followers,and studies its existence and finally proves the existence of weakα-core of multi-leadermulti-follower games.

关 键 词：主从博弈 α-核 弱α-核 局部FS-majorized 

分 类 号：O225[理学—运筹学与控制论]