【作者】 王艳；

【导师】 张雪峰； 徐心和；

【作者基本信息】 东北大学 ， 运筹学与控制论， 2008， 硕士

【摘要】 博弈问题要比控制和决策问题更加复杂和难于求解,因此也更富于挑战性。面向各种博弈问题建模和求解的博弈论已有半个多世纪的快速发展,并且取得了一系列具有里程碑意义的研究成果,对于经济学和相关领域的发展起到了巨大的推动作用。在简述博弈论最主要研究成果的基础上,总结了博弈论分析的精髓和基本模式——“理性-预测-均衡”。然而面对大规模的复杂的动态博弈系统,如象棋博弈,现有的博弈论却不能进行着法的求解,由此暴露出现有博弈论的一些局限性问题。为此应将博弈论与机器博弈加以结合,以此推动博弈论的拓展,开创博弈论应用的新局面。本文的研究是属于事件对策论的初期研究。内容如下：首先是绪论,主要介绍了博弈论的产生与发展,博弈论的里程碑成果,合作博弈与非合作博弈,并简要介绍了本文的工作；接着介绍了非合作博弈的理论基础,包括博弈论的基本概念,博弈类型与理论结构,纳什均衡的相关知识,矩阵对策的定义及相关定理,矩阵对策的数学模型,矩阵对策的线性规划求解；然后是博弈论的精髓与局限性分析,主要从博弈论中的理性问题,“理性-预测-均衡”——博弈论的精髓,博弈论的局限性分析,有限理性对博弈问题的影响等方面进行分析；再次是主要通过数学分析与数值分析对比联系到博弈论与机器博弈的关联问题,从而得出用数值方法求解博弈论问题；进而主要介绍非合作博弈理论在牛角棋上的应用,从牛角棋机器博弈原理,牛角棋机器博弈程序设计等方面具体分析；最后总结全文：应将博弈论与机器博弈加以结合,推动博弈论的拓展,开创博弈论应用的新局面。结合本文的研究可以为事件对策论的深入研究起到一个铺垫作用,对事件对策论和机器博弈的应用研究有一定的参考价值。更多还原

【Abstract】 The game issues are more complicated and difficult to be solved than the control and decision problems, therefore they are more challenging. The game theory that oriented to the formulation and solution of various game issues has undergone over half a century of fast development, and has gained a series of achievement milestones. So it has played a great positive role in the development of economics and relevant fields. Based on the main results of the game theory, the essence and the basic model of game theory are summarized, i.e. rationality-prediction-equilibrium. But when facing the complicated dynamic game systems, such as chess game, it is hard to solve one move by game theory. Thus some limitations of the theory are shown. Therefore, the game theory and computer game should be combined, by this way we can promote the extension of the theory and create a new situation for the applications of game theory.The study of this paper belongs to the initial study of the event game theory. First, it mainly introduces the emergence and development of the game theory, its achievement milestones, cooperative game and non-cooperative game, and briefly introduce the job of this paper. Second, it introduces the theoretical basis of the non-cooperative game, which includes the basic concepts, the types and the theoretical structure of the game theory, the related knowledge of nash equilibrium, the definition, related theorem, the mathematical model and linear programming solution of matrix game. Third, it is the essence and limitation analysis of game theory, and mainly analyze from some aspects such as the rational problem of game theory, the essence and the basic model of game theory--rationality-prediction-equilibrium, the influence of the limited rationality to the game theory. Fourth, it connects the game theory and computer game theory by analyzing mathematical analysis and numerical analysis, so we obtain that we can solve the game theory by numerical methods, then apply the non-cooperative game theory to the horn, it mainly concludes the game theory and the programming of horn. In the last part, a summary of this paper is given, and the expectation of scientific research in aftertime is given. Combined with the study of this paper, we can give a foreshadowing role to the event game theory, and have certain reference value to the application research of the computer game theory and the event game theory.更多还原