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乒乓球比赛战术的博弈分析

Game Theoretic Analyses of the Tactics in Table Tennis Matches

【作者】 陈家鸣

【导师】 苏丕仁;

【作者基本信息】 北京体育大学 , 体育教育训练学, 2008, 博士

【摘要】 本研究主要运用博弈论的基本原理、思维方法和分析方法,从宏观角度来探讨乒乓球比赛战术运用的微观问题;目的是使我国从事乒乓球运动的教练员、运动员和科研人员,在面临对抗性强、竞争激烈的重大比赛中,开阔思路,提高战术思维素养,减少比赛决策失误,提高获胜几率;进一步丰富乒乓球比赛战术的分析理论,为中国乒乓球队在2008年北京奥运会上取得优异的成绩提供理论支持。本研究主要有以下结论:(1)根据博弈论的基本原理,将乒乓球竞技博弈定义为“零和博弈”;在竞技比赛实践中,根据双方运动员博弈过程诸因素的关系分析,乒乓球竞技过程既有动态博弈,又有静态博弈;将乒乓球比赛战术运用过程中的博弈定义为:“完全信息动态博弈”、“不完全信息静态博弈”、和“完全且不完美动态博弈”;(2)乒乓球竞技博弈中战术选择和战术运用过程的本质和特征是,既有战术行动相继发生的序贯博弈,也有战略行动同时发生的同时博弈,以及两种博弈都存在的混合博弈;在乒乓球比赛战术选择和运用的序贯博弈过程中,可以用逆向归纳法,即“向前展望,倒后推理”的方法,找到博弈均衡。均衡是一种描述,也是一个过程,但不是一个指标;(3)三种简单的数学方法:反映函数法、最小最大法和直线交叉法,在进行战术理论研究中具有可操作性。在理论上找到博弈的均衡解要应用到实践中去,那就是,在乒乓球比赛战术运用实践中,应该努力做到:当我方掌握主动时,要抢先打破均衡赢得每一分球,直至比赛胜利;当我方迫于被动时,又要抢先建立均衡进入相持,然后再抢先打破这种均衡,转为主动;(4)运动员的“个体理性”、主观能动性和个性心理特征与运动员的风险偏好及风险承担能力密切相关,影响比赛战术的选择和运用;(5)路径依赖问题存在于乒乓球比赛战术运用的过程中,它也是影响比赛胜负的重大因素之一;运动员要突破自身的路径依赖问题应遵循以下原则:①选择正确的混合策略;②不能依赖对手的随机化;③提高技术,随之改变战术使用概率。

【Abstract】 The research,mainly by means of principles of the game theory,the thinking methodology and analytical methodology,probes into the microcosmic tactics in table tennis matches from the viewpoint of a totally new macroscopically angle so that the table tennis coaches,athletes and research specialist staff in our country can widen their thoughts,improve their tactical attainment,reduce their decision-making misplays in important matches,increase their winning probability,further enrich their analytical means in table tennis matches.The research is intended as well to provide theoretical support for Chinese table tennis team to achieve great success in 2008 Beijing Olympic Games.The conclusions of the research are as follows:(1) From the angle of the game theory,the table tennis competitive game theory is "zero-sum game".The table tennis competitive process can be divided into dynamic game theory and static game theory;the game theory in the course of the exertion of table tennis tactics can be defined as complete information dynamic game theory and incomplete information static game theory and complete but imperfect dynamic game theory.(2) After analyzing the game theory,the thesis reveals the natural characteristics of technical choice and technical exertion in table tennis competitive game theory,in which there are successive game theory and spontaneous game theory and the mixed game theory that include both of them.In the course of successive game theory,every player can take advantage of the reverse induction of "expecting forward,reasoning backward" to achieve balance.Balance is both a description and a process,but not a guide line.(3) The purpose of game theory analysis is to find out how to achieve balance. As a result,the thesis introduced three comparatively simple mathematical techniques that are often used in the game theory.They are reflective function technique, minimum and maximum technique and straight line interior extrapolation technique, which is quite maneuverable in the tactical theoretical research.However,the task has not been completed when the balance is achieved theoretically until it is put into practice.(4) The thesis,from the viewpoint of players’ rationality,subjective initiative and individual psychological features,uses the game theoretical analysis to analyze the players’ venture favor and their ability to undertake the ventures,which is a new trial.(5) The problem of dependence naturally exists everywhere in society,which is seldom realized in competitive sports,especially in table tennis tactics.In this thesis, the writer puts forward the principles and solution as to how to break through the problem of dependence.

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