  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.
