双矩阵博弈完美平衡的稳定性与灵敏度分析

【作者】 郑磊；

【导师】 杨辉；

【作者基本信息】 贵州大学 ， 应用数学， 2007， 硕士

【摘要】 本文研究了双矩阵博弈完美平衡的稳定性，运用线性规划的方法对模型进行灵敏度分析，然后通过双矩阵博弈的完美平衡与线性规划的联系对双矩阵博弈的完美平衡做稳定性的分析。第一章为背景知识，介绍了博弈论的出现，发展，以及现况，描述了博弈论的类型以及理论结构。叙述了非合作博弈论的一些成果，并通过经典例子来认识非合作博弈。第二章是预备知识，主要介绍本文用到的一些相关知识，说扰动博弈，完美平衡的概念以及相关的引理。第三章是应用线性规划的方法如何来验证双矩阵博弈的完美平衡点。第四章用线性规划的方法对双矩阵博弈的完美平衡做了稳定性的研究。本章主要是对线性规划的模型进行灵敏度分析，然后通过线性规划的模型和双矩阵博弈的联系分析双矩阵博弈完美平衡的稳定性。更多还原

【Abstract】 In this paper,we research the stability of perfect equilibrium of bimatrixgame by applying linear programming. Specifically, we research the stability andsensitivity analysis of perfect equilibrium of bimatrix game through the relation ofperfect equilibrium and linear programming.The first chapter is the background knowledge. We introduce the game theoryappearance, development, present situation and it’s type as well as the theory structure.In addition, we introduce some achievements and classical examples of non-cooperation game, through which we can obtain more understanding to the non-cooperation game.The second chapter is preliminary knowledge, which mainly contains somerelated knowledge, such as perturbation game, perfect equilibrium concept and somelemma.In the third chapter, we confirm the perfect equilibrium of bimatrix game byapplying linear programming.In the fourth chapter, we analyse the stability of perfect equilibrium of bimatrixgame by applying linear programming. This chapter mainly carries on the sensitivityanalysis to the linear programming model. Then we analyze the stability of perfectequilibrium of bimatrix game through the relation of the linear programming modeland bimatrix game.更多还原