基于集值分析的某些向量值广义博弈均衡问题研究

The project mainly deals with equilibrium problems of games with the discontinuous vector payoff. First, based on the background of the evolution and reconstruction of the manufacturing ecosystem in the Internet era, the mathematical model of the relevant game is established or reformed. Then, by using the model as the starting point, and by using the mathematical theory as the tool, we will systematically analyze and study the game theory. We will focus on the existence of equilibriums for games with discontinuous vector payoff, as well as, the fuzzy logic is introduced to discuss such existence in fuzzy strategy sets. Moreover, we consider the case that the strategy set has no topological structure or algebraic structure. In order to facilitate the application, some algorithms will be targetedly explored. The mathematical modeling will be based on "13th Five-Year" planning of manufacturing in Zhejiang province so that one can widely collect effective information and data and process the information and data by using the methods of analysis, differentiation and analysis.. On theoretical research, Set-valued analysis will be selected as a platform, and nonlinear analysis and other mathematical theory will be used as a tool. While deepening research of the theory of fixed point of set-valued operators, set-valued optimization and quasi variational inequality, the fuzzy analysis and market mechanism design will be applied. We will focus on the research of game theory with the purpose of solving the actual problems, in order to promote scientific management to develop in depth, and provide scientific basis for the relevant decision-making departments.

项目主要涉及向量值支付函数的广义博弈的均衡问题，理论研究方面：重点研究不连续向量值支付的Nash均衡的存在性，同时引入模糊逻辑，主要研究策略集在模糊环境下的均衡问题，并考虑策略集不具拓扑结构或代数结构的情形；初步探讨均衡点集的稳定性；为了方便应用，将有针对性的研究一些算法问题。为了理论的实用性，最后将实证研究。理论研究为本项目的主要研究内容，将以集值分析为平台，以不动点定理等数学理论为工具，在深化集值函数微积分、集值算子的不动点、集值优化以及拟变分不等式等非线性分析理论研究的同时，采用模糊分析和市场机制设计等手法。实证研究将以互联网时代制造生态系统的演变与重构为背景，以浙江制造业为实例，广泛采集有效信息和数据，运用分析、辨析和证析的方法，建立或改造利用相关博弈的数学模型，然后在此基础上，运用所获理论处理某些实际问题。目的是深化博弈理论研究，以实际问题为背景和驱动，推动管理科学向纵深发展。

项目主要涉及向量值支付函数的广义博弈的均衡问题，重点研究不连续向量值支付的Nash均衡的存在性，同时研究微分博弈的均衡存在性和稳定性，以及值函数的存在星等；也有引入模糊逻辑，研究策略集在模糊环境下的均衡问题，并考虑策略集不具拓扑结构或代数结构的情形；初步探讨均衡点集的稳定性；为了方便应用，将有针对性的研究一些算法问题。为了理论的实用性，最后将实证研究。理论研究以集值分析为平台，以不动点定理等数学理论为工具，在深化集值函数微积分、集值算子的不动点、集值优化以及拟变分不等式等非线性分析理论研究的同时，采用模糊分析和市场机制设计等手法。实证研究将以互联网时代制造生态系统的演变与重构为背景，以浙江制造业为实例，广泛采集有效信息和数据，运用分析、辨析和证析的方法，建立或改造利用相关博弈的数学模型，然后在此基础上，运用所获理论处理某些实际问题。目的是深化博弈理论研究，以实际问题为背景和驱动，推动管理科学向纵深发展。