  We consider a symmetric multi-players zero-sum game with two strategic
variables. There are $n$ players, $n\geq 3$. Each player is denoted by $i$. Two
strategic variables are $t_i$ and $s_i$, $i\in \{1, \dots, n\}$. They are
related by invertible functions. Using the minimax theorem by \cite{sion} we
will show that Nash equilibria in the following states are equivalent.
  1. All players choose $t_i,\ i\in \{1, \dots, n\}$, (as their strategic
variables). 2. Some players choose $t_i$'s and the other players choose
$s_i$'s. 3. All players choose $s_i,\ i\in \{1, \dots, n\}$.
