具有连续分布市场的网络寡头模型研究  

Research on the Network Oligopoly Models with Continuous-variable Markets

作　　者：王能发[1] 杨哲[2,3] WANG NENGFA;YANG ZHE(School of Mathematics and Statistics,Guizhou University of Finance and Economics/Guizhou Key Laboratory of Big Data Statistical Analysis,Guiyang 550025,China;School of Economics,Shanghai University of Finance and Economics,Shanghai 200433,China;Key Laboratory of Mathematical Economics(SUFE),Ministry of Education,Shanghai 200433,China)

机构地区：[1]贵州财经大学数学与统计学院/贵州省大数据统计分析重点实验室,贵阳550025 [2]上海财经大学经济学院,上海200433 [3]上海财经大学数理经济学教育部重点实验室,上海200433

出　　处：《应用数学学报》2025年第1期53-68,共16页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(批准号:72371146);贵州省大数据统计分析重点实验室(批准号:黔科合平台人才[2019]5103);贵州省高等学校系统建模与数据挖掘重点实验室(批准号:2023013);贵州省高层次创新型人才项目(批准号:黔科合平台人才-GCC[2022]020-1)资助。

摘　　要：本文扩展有限多个市场的网络寡头为具有无限多个市场的情形,将构建具有连续分布市场的网络寡头模型.在完全非合作的假设下,首先证明Cournot-Nash均衡的存在性.进一步,假定厂商集合存在一个联盟结构,凭借定义联盟成本函数和联盟利润函数,我们构建了一个基于联盟结构的非合作博弈,并证明了此博弈中Nash均衡的存在性.新的网络寡头模型和Nash均衡的存在性证明为本文的主要贡献.In this paper,we extend the network oligopoly with finitely many markets to the model with infinitely many markets,and propose the network oligopoly model with continuous-variable markets.Under the fully noncooperative hypothesis,we first prove the existence of Cournot-Nash equilibria.Furthermore,we assume that there exists a partition of the set of firms.By defining the coalitional cost function and coalitional profit function of every coalition,we establish a noncooperative game basing the coalition structure,and prove the existence of Nash equilibria.New network oligopoly models and Nash equilibrium existence theorems are our main contributions.

关 键 词：网络寡头 连续分布市场 联盟结构 NASH均衡 存在性定理 

分 类 号：O225[理学—运筹学与控制论]