乒乓球序贯行动博弈的纳什均衡

Sequential Action Game's Nash Equilibrium in Table Tennis Competition

运用文献资料法、专家访谈法奠定了研究基础,通过录像观察、数理统计进行了比赛战术行为信息的数据采集。以博弈论为理论基础和分析工具确定了分析的基本框架,对世界优秀男子乒乓球选手竞赛过程中的落点战术行为进行了博弈实证研究,探求乒乓球运动员在比赛中战术行为决策时的理论依据。研究中根据运动员的战术决策思维特征,构建了乒乓球落点战术行为序贯博弈分析的拓展式(博弈树)模型,运用极大极小算与逆推均衡算法进行了博弈树的求解。研究得出:博弈论可以为乒乓球战术研究提供一个新的理论视角,并可以作为基础理论对乒乓球运动实践进行理论分析,探究乒乓球运动的内在规律;通过乒乓球落点战术行为可以构建序贯行动的博弈树模型,用最大最小值与逆推均衡原则来寻找纳什均衡路径;通过特定两名乒乓球运动员之间的纳什均衡来预测下一场比赛的战术行为决策特征,有利于战术行动方案决策。

Based on game theory and other analysis tools, this paper analyzed world top male table tennis players＇ ball placement tactical behavior in competition and explored their decision-making foundation by the methods of literature review, expert interview, video observation, mathematic statistics. According to the tactical decisions think- ing characteristics of athletes, this study constructed a table tennis ball placement tactical behavior sequential game analysis of expanding type（ game tree） model and used mini-max calculation and reversed equalization algorithm for the solution of the game tree. Conclusions ： Game theory can provide a new theoretical perspective for the research on table tennis tactics and can be used as a basic theory for table tennis practice through theoretical analysis to study the inner laws of table tennis. Table tennis ball placement tactical behavior can build a sequential action game tree model, then use the largest minimum and reversed balance principle to find the Nash equilibrium path. Through specific two table tennis players＇ Nash equilibrium to predict tactics behavior decision-making characteristics of the next match is advantageous to the tactical action decision.