多主从群体博弈中合作均衡的存在性  

Existence of Cooperative Equilibria for Multi-leader-multi-follower Population Games

作　　者：张弦 ZHANG XIAN(University of Shanghai for Science&Technology Business School,Shanghai 200093,China)

机构地区：[1]上海理工大学管理学院,上海200093

出　　处：《应用数学学报》2022年第2期197-211,共15页Acta Mathematicae Applicatae Sinica

摘　　要：基于Scarf,Kajii关于n-人非合作博弈中的合作均衡存在性定理,越来越多的研究表明,对非合作博弈的合作均衡研究是有必要的.本文综合Sandholm的群体博弈模型以及Yang和Ju证明的多主从博弈的合作均衡存在性定理,旨在详细研究多主从群体博弈的合作均衡.首先,在多主从群体博弈中引入合作均衡的概念,并通过Kajii的命题2证明其存在性定理.然后,将本文的结论退化为群体博弈的合作均衡存在性定理以及单主多从群体博弈的合作均衡存在性定理.最后,给出群体博弈和多主从群体博弈相应的算例分析.Based on the existence theorem of cooperative equilibria for n-person noncooperative games by Scarf and Kajii,more and more studies show that its necessary to study the cooperative equilibrium of non-cooperative games.We integrate the population games model by Sandhlom and the existence theorem of cooperative equilibrium for multileader-multi-follower games proved by Yang and Ju,aiming at studying the cooperative equilibrium of multi-leader-multi-follower games in detail.First,we introduce the concept of cooperative equilibrium in multi-leader-multi-follower population game and prove its existence theorem by Proposition 2 in Kajii.Then,we degenerate the conclusion of this paper into the existence theorem of cooperative equilibrium in population games and the existence theorem of cooperative equilibrium in single-leader-multi-follower population games.Finally,we give the corresponding examples analysis of population games and multi-leadermulti-follower population games.

关 键 词：多主从群体博弈 合作均衡 存在性 

分 类 号：F224.32[经济管理—国民经济] O225[理学—运筹学与控制论]