In this report, some properties of the set of Nash equilibria (NEs) of $2 \times 2$ zero-sum games are reviewed. In particular, the cardinality of the set of NEs is given in terms of the entries of the payoff matrix. Moreover, closed-form expressions for the NE strategies and the payoff at the NE (the value of the game) are provided in terms of the entries of the payoff matrix. The results presented in this report are not necessarily new knowledge, as they follow from the definition of the NE after some tedious calculations. Nevertheless this synthetic presentation is original in the literature.

翻译：在本报告中,审查了Nash equilibria (NES) 系列游戏的某些属性,即2美元2倍2和零和游戏,特别是,一套NES的主要属性是报酬矩阵的条目;此外,NE 战略和NE(游戏价值)的封闭形式表达方式是报酬矩阵的条目;本报告中介绍的结果不一定是新的知识,因为这些结果是在经过一些烦琐的计算后对NE的定义得出的;不过,这种合成的表述在文献中是原始的。