对足球比赛中射门的博弈分析以及统计检验

Game Analysis and Statistical Tests about the Shooting in Soccer

首先建立了一个数学模型,模拟足球比赛中球员在射门时和门将之间的博弈关系;之后,通过分析推导,找到了模型的一组混合策略纳什均衡解;根据对这组解的进一步推理分析,得出了射门球员和守门员的策略选择倾向;最后,利用从比赛中收集得到的统计数据,对这组混合策略纳什均衡解分别从局部和整体上进行了统计学意义上的检验.

This paper established a mathematical model to simulate the game relationship between the shooting player and the goalkeeper. Then, a mixed strategy Nash equilibrium solution can be found in the model. According to the analysis of this model, the choosing tendency of the shooting player and the goalkeeper can also be obtained. Finally, from the local and global, this group of mixed strategy Nash equilibrium solution will be tested based on the data that were collected from the soccer games.