排球扣球与单人拦网博弈的混合策略纳什均衡研究
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摘要
基于对博弈论的理解,将"扣球--拦网"这一对弈行为放入博弈分析法框架内进行研究,以探求排球比赛中个人战术行为应用的最优规律为研究目的,运用文献资料法、专家访谈法、录像观察法、数理统计法等研究方法对高水平女排比赛中这一博弈现象进行了研究。得出结论:扣球--拦网(单人拦网)"属于完全信息静态博弈中的双人零和博弈;这一博弈中的参与者均使用混合策略,而这一混合策略博弈可以通过图解法求得纳什均衡;参与者应按照纳什均衡的解以及对方的决策情况安排自己的应对决策,从而获得最佳收益。
Based on the understanding of game theory, this paper studies the behavior of spiking-blocking in the framework of game analysis. The purpose of this study is to explore the optimal law of individual tactical behavior in volleyball matches. The game phenomenon in high-level women's volleyball matches is studied by using the methods of literature, expert interviews, video observation and mathematical statistics. It is concluded that spiking-blocking(single blocking) belongs to the two-player zero-sum game in the static game of complete information. All participants in this game use mixed strategy, which can obtain Nash Equilibrium by graphical method, and should arrange their own coping decisions according to Nash Equilibrium solution and the other party's decision-making situation, so as to obtain the best performance.
Based on the understanding of game theory, this paper studies the behavior of spiking-blocking in the framework of game analysis. The purpose of this study is to explore the optimal law of individual tactical behavior in volleyball matches. The game phenomenon in high-level women's volleyball matches is studied by using the methods of literature, expert interviews, video observation and mathematical statistics. It is concluded that spiking-blocking(single blocking) belongs to the two-player zero-sum game in the static game of complete information. All participants in this game use mixed strategy, which can obtain Nash Equilibrium by graphical method, and should arrange their own coping decisions according to Nash Equilibrium solution and the other party's decision-making situation, so as to obtain the best performance.
引文
[1]迪克西特·斯克斯著,蒲勇健等译.策略博弈(第二版)[M].北京中国人民大学出版社,2009,1:36-41.
[2]罗云峰.博弈论教程[M].北京:清华大学出版社;北京交通大学出版社,2007,8:41-56.
[3]李光久,李昕.博弈论简明教程[M].江苏:江苏大学出版社,2013,1:35-44.
[4]刘文明,杨忠令,楼恒阳.网球战术行为“混合策略”理论验证[J]北京体育大学学报,2014,37(8):124-130.
[5]国际排联[EB/OL].[2018-09-14]http://www.fivb.org/en.FIVBVolleyball Women's World CupJapan,2015.
[6]郝霖霖,葛春林,钱俊伟,等.排球竞赛中战术行为决策的混合策略纳什均衡研究[J].南京体育学院学报,2015,29(1):108-113.
[7]刘文明,唐建军.乒乓球竞赛发球与接发球博弈的混合策略纳什均衡研究[J].北京体育大学学报,2012,35(8):134-138.
[2]罗云峰.博弈论教程[M].北京:清华大学出版社;北京交通大学出版社,2007,8:41-56.
[3]李光久,李昕.博弈论简明教程[M].江苏:江苏大学出版社,2013,1:35-44.
[4]刘文明,杨忠令,楼恒阳.网球战术行为“混合策略”理论验证[J]北京体育大学学报,2014,37(8):124-130.
[5]国际排联[EB/OL].[2018-09-14]http://www.fivb.org/en.FIVBVolleyball Women's World CupJapan,2015.
[6]郝霖霖,葛春林,钱俊伟,等.排球竞赛中战术行为决策的混合策略纳什均衡研究[J].南京体育学院学报,2015,29(1):108-113.
[7]刘文明,唐建军.乒乓球竞赛发球与接发球博弈的混合策略纳什均衡研究[J].北京体育大学学报,2012,35(8):134-138.