Nashtopes and their A-discriminants

An $n$-player game in normal form is said to be of format $\boldsymbol{d} = (d_1, \dots, d_n)$ if the $i$-th player has $d_i$ options for $1 \le i \le n$, and is said to be balanced if $d_n - 1 \le \sum_{i=1}^{n-1}(d_i - 1)$. The Nash equilibria of the game correspond to solutions of the system of i