网球单打比赛发球与接发球战术博弈的混合策略纳什均衡研究

Study on the Mixed Strategy Nash Equilibrium in the Game of “Serve-Serve Reception” in Tennis Singles Competition

混合策略纳什均衡是博弈论中比较核心的概念,有着极其重要的作用。文中采用文献资料法、专家访谈法和数理统计法对网球单打比赛发球与接发球战术博弈中的"混合策略纳什均衡"进行了研究。研究得出:网球单打比赛的战术博弈是一种严格的双人零和博弈,在网球单打比赛的战术博弈中,要通过混合策略的使用来突破战术运用具有路径依赖的现象,即必须随机选择策略和重视选择各个策略的概率分布,让自己的策略选择不能带有很强的规律性。完全信息静态博弈中求预期得益的方法和反应函数可以用来求解网球单打比赛战术博弈的混合策略纳什均衡,满足纳什均衡的混合策略互为双方针对对手随机化策略的最佳对策。

The mixed strategy Nash equilibrium is the core concept in game theory and plays an extremely important role. This paper studies the mixed strategy Nash equilibrium in the game between serving and receiving of tennis singles by using the method of documentation, expert interview and mathematical statistics. The study concludes that the tactical game of tennis singles matches is a strict double zero sum game. In the tactical game of tennis singles game, the use of mixed strategy can be used to break through tactics and use of path dependence, namely must choose random selection strategy and pay attention to the probability distribution of each strategy, make their own strategy choice not with great regularity. The method of the expected benefit in the static game of complete information can be used to solve the mixed strategy Nash equilibrium of the tactical game of tennis singles game, the mixed strategy that satisfies Nash equilibrium is the best countermeasure of each other＇s randomized strategy.