若干广义Nash均衡问题的非线性分析方法和应用

项目名称： 若干广义Nash均衡问题的非线性分析方法和应用

项目编号： No.71471051

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 管理科学

项目作者： 洪世煌

作者单位： 杭州电子科技大学

项目金额： 62.5万元

中文摘要： 广义Nash均衡存在许多有意义且值得探讨的问题。本项目从数学角度出发，在非线性分析的框架下，以集值分析为平台，强化利用不动点理论、集值优化及(拟)变分不等式等数学工具，着重研究广义Nash均衡问题均衡点集的稳定性，如结构稳定、Liapunov稳定及其指数稳定和渐近稳定等，创造判断稳定性的新方法。为了结构稳定必须讨论均衡模型的连续性，为了利用微分方程的相关理论，必须讨论集值函数的可微性并建立相应集值微分方程模型。稳定性以存在性为前提，因此研究均衡点的存在性不可避免，本项目主要探讨不连续支付函数和向量值支付函数的存在性，同时引入模糊逻辑，研究策略集在模糊环境下均衡点的存在性，目的是使理论更完善，应用范围更广泛。为了应用，将有针对性的研究一些算法问题，如局部Newton法等。最后将结果应用在区域雾霾联防与治理的机制方面，创建或改造利用相关博弈模型并进行理论分析和算法设计，为政府决策提供科学依据。

中文关键词： 纳什均衡；对策论；非合作博弈论；不动点理论；非线性分析

英文摘要： There are many interesting issues related to the generalized Nash equilibrium problem, some arising from its mathematical challenges some from its typical applications. In this project, from the mathematical point of view, we will consider the structural stability，Liapunov's stability exponential stability and asymptotically stability of the set consisting of equilibria points.Moreover,we shall consider the continuity of the equilibria point set for the structural stability, also, for the applications of the corresponding properties of differential equations, we have to discuss the differentiability of the equilibria point set operators and to establish the set-valued differential equations.The existence of equilibria points and its algorithm will be considered for the geberalized Nash equilibriums with discontinuous payoff functions or/and vector payoff functions in the nonlinear analysis framework and in the set valued analysis platform.In addition, via the fuzzy logic we discuss the existence of equilibria points with fuzzy stratagy sets.Finally,our results will be used in establish a model for environmental protection. From some real-world applications, a number of problems in economics can be formulated as games with discontinuous payoff functions. The best known of some classical problems are probably Bertrand's model of duopolistic price competition (Bertrand 1883) and Hotelling's model of duopolistic spatial competition (Hotelling 1929. In addition, as a matter of fact, traditional game theory is anchored on binary (Aristotelian) logic and the fully rational behavior assumption. Fuzzy logic is able to accommodate many of the binary-logic related dilemmas in crisp game theory, e.g. Prisoner's Dilemma game. In general, in real games the players do not behave as fully rational decision makers, rather they follow the principle of bounded rationality. Consequently, standard theorems such as those found in Nash,or Arrow-Debreu , cannot be applied to establish the existence or stability of an equilibrium (pure or mixed). Now while in many of these games equilibria can be constructed, rendering the existence and stability questions moot.In this project we will propose some methods of studing the existence, stabilty and algorithm of the style generalized Nash equilibrium.

英文关键词： Nash equilibrium;Game theory;noncooperative game theory;Fixed point theory;Nonlinear analysis