乒乓球竞赛发球与接发球博弈的混合策略纳什均衡研究

纳什均衡是博弈理论最为核心的概念,采用文献资料、专家访谈、录像观察等研究方法对乒乓球战术行为中的"混合策略纳什均衡"进行了研究,研究得出:乒乓球战术行为博弈的"混合策略"是纯策略的概率组合,混合策略是连续策略的一种特例。最优反应分析能够用来求解乒乓球战术行为博弈的混合策略均衡,在运动实践中乒乓球运动员(博弈方)博弈过程中都存在各自的最优反应规则,并能够根据这一规则构建最优反映曲线,最终得出乒乓球战术行为混合策略纳什均衡解。乒乓球战术行为中"混合策略"的重要性在于揭示了博弈双方也就是乒乓球运动员一定不能使自己的战术行为表现出很强的规律性,因为一旦被对手发觉那么就将处于劣势状态。

Study on the Mixed Strategy Nash Equilibrium in the Game of "Serve-Serve Reception" in Table Tennis Competition

Nash Equilibrium is the core concept of game theory.Video observation,interview and literature were used to study the mixed strategy Nash Equilibrium in the tactical behavior of the table tennis game.The results are as below:As the mixed strategy game,the table tennis tactic behavior game is the probabilistic combination of pure strategies.Mixed strategy is a special case of continuous strategy. The optimal reaction analysis can be used to solve the mixed strategy Nash Equilibrium in the tactical behavior of the table tennis game.Table tennis players in sports practice represents the respective optimum reaction rule in the game process,which builds the optimum curve reflect the behavior of table tennis tactics mixed strategy Nash Equilibrium solution.The importance of mixed strategy Nash Equilibrium in the tactical behavior of the table tennis game lies in the strategy that once the player shows a strong regularity,the opponents can easily find the rule and will be at a disadvantage status.