摘要
博弈论是研究利益冲突情况下决策分析的科学。博弈论是对现实生活的高度抽象,这种抽象性使得博弈论在现实应用中有了广泛的背景。在理论与实践的相互推动中,博弈论得到了发展并且与实践越来越接近。
在传统博弈中,局中人的支付函数都是通过某些确定的数值来体现的。但是在现实问题中局中人在决策之前对于博弈的结果的预测并不是一个精确的数值。1965年Zadeh提出了模糊集理论,为处理现实中不确定现象提供了有力的工具。随后,研究人员将其引入博弈论的研究中并发展成博弈论研究中一个重要的分支—模糊博弈。根据模糊集与博弈论结合点的不同,模糊博弈的含义也是不同的。本文主要研究支付函数为模糊集,策略(联盟)为清晰集的博弈问题。
本文的主要研究内容如下:
1)回顾博弈论的产生和发展的历史,分析了模糊博弈论产生的背景和研究的必要性和意义,对国内外的研究状况进行了评述。
2)介绍了关于模糊集的一些基本概念,模糊数的性质和运算,对模糊数的比较方法的分类、评价准则进行了重点分析。
3)根据模糊数比较方法的分类,研究了模糊矩阵博弈的均衡问题。将经典非合作博弈拓展到模糊集上,借助模糊优先关系定义了Nash均衡的概念,证明其存在性。从模糊集理论的思想出发提出模糊均衡的概念,有效避免了Nash均衡稳定性差、多重性等缺陷。
4)将模糊非合作博弈的理论应用于建立供应链合作伙伴关系中,并给出了求解规模较大的模糊非合作博弈模糊均衡解的改进遗传算法,通过实例验证了其有效性。
5)在经典合作博弈的基础上,对其相关概念进行拓展,重新定义了模糊超可加、模糊分配、模糊优超、模糊核心等概念,找出了模糊核心存在的充要条件,证明了模糊凸合作博弈核心是非空的。
最后总结了论文的主要研究工作和结论,对今后的研究工作进行了展望。
Game theory is the science of strategy, the study of decision-making in conflicts of interest. It has broad applications with the background that it abstractly represents our real life. Game theory and practices, mutually boosted, have been well developed and combined more tightly.
In traditional game theory, each player’s payoff function is given fixed. However in reality, players usually hold uncertain estimated game-result. Fuzzy set theory, grounded by Zadeh in 1965, is a great utility to handle uncertainty of real problems. It is introduced into game theory research, and the combination forms an important branch-fuzzy Game, which has varied meanings according to different combination types. This dissertation addresses research in game theory with regard to payoff function in fuzzy-set and strategy (union) in crisp-set.
The main contributions of this dissertation are as follows:
1) The origin and develop history of game theory are reviewed, also the background and the necessity and significance of the research are analyzed, including the domestic and overseas research situations.
2) Some basic concepts, as well as the properties and operations of fuzzy set, are introduced. As an emphasis, fuzzy-number-comparison classification and evaluation criteria is interpreted.
3) Based on the different classification of fuzzy-number, equilibrium problem of fuzzy matrix game is studied. And the classical game theory is extended to fuzzy set field, with definition of the Nash equilibrium concept via fuzzy preference relationship and proof of its existence. Meanwhile, the concept of fuzzy equilibrium is proposed, from the viewpoint of fuzzy set theory.
4) Application of uncooperative fuzzy game theory in establishment of cooperative supply chain partnership is conducted, and an improved genetic algorithm as large-scale of uncooperative fuzzy game equilibrium solver is designed and verified effect by cases.
5) Some related concepts on the basis of classical cooperative game are extended, with redefinition of fuzzy superadditivity, fuzzy imputation, fuzzy domination and fuzzy core, etc. The sufficient-necessary condition for fuzzy core existence is revealed; and fuzzy core unemptiness of cooperative game is proved.
As a conclusion, the dissertation finally summarized the research achievements, and discussed the future work.
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