【作者】 张丽敏；

【导师】 高作峰；

【作者基本信息】 燕山大学 ， 运筹学与控制论， 2012， 硕士

【摘要】 对策论中，合作对策得到了广泛的关注和研究，随机合作对策作为对策论的一个分支，自Suijs等人在1995年引入后，主要研究在合作对策形成过程中对局中人的吸引力的大小为基础的合作对策，吸引了不少学者的研究，并取得了很好的成果。论文主要是在随机合作对策模型下加入凸合成对策理论，建立了凸合成随机合作对策。在随机合作对策条件下，介绍了它的凸性和超可加性，并给出了随机合作对策的核、核仁和Shapley值的概念，讨论了它们的性质。将凸合成对策与随机合作对策结合，给出了凸合成随机合作对策的核仁、核心和稳定集结构，并通过对优超定义的推广，给出了凸合成随机合作对策的弱核心与弱稳定集，对它们的性质和关系进行了研究。首先介绍对策论的发展史，论文产生的背景以及论文研究的实用价值。其次介绍了与论文相关的随机合作对策的基础知识。研究随机合作对策的凸性和超可加性，给出了随机合作对策的核、核仁与Shapley值的概念及性质，为下文研究凸合成随机合作对策奠定了理论基础。最后建立了凸合成随机合作对策的模型，给出了核心、稳定集和强ε核心的概念，并给出了它的几种不同解的结构以及它们的性质与关系；将优超的概念推广，定义了弱优超，并给出了它的弱核心和弱稳定集的概念和它们之间的关系。更多还原

【Abstract】 In game theory, cooperative game has received a concern and become a researchfocus. Stochastic cooperative game, as a branch of game theory, it has attracted manyscholars’interest, and some significant results are obtained.The main paper is the stochastic cooperative game model by adding convexcompound game theory, set up convex compound stochastic cooperative game, under thecondition in the stochastic cooperative game, introduce their convexity and superadditive,we present the new concepts of kernel，nucleolus and Shapley value, and discuss theproperties of them. Then we combine the convex compound game and stochasticcooperative game, give their structure of nucleolus, core and stable set, and by expandingthe definition of dominance, we present the new concepts of weak core and weak stableset, study their properies and the relations of the core and stable set.First, providing histories of classical games theory, background and practical value ofthe paper.Second, introduce the stochastic cooperative game which related to the thesis,introduce the convexity and superadditive of the stochastic cooperative game, focusing ontheir concepts and characteristics of kernel and nucleolus for the following.In the last part, we define the convex compound stochastic cooperative game model,define the concept of core, strong ε-core and stable set, study the properties of them, thengive the relations between the core and stable set. Then we define the weak dominance,give the concepts of weak core and weak stable set, and the relations between them.更多还原