Solution
= Solution
For probability <vectors> $p,q$, they are optimal with value $v$ exactly when
$$
p^TAe_j\ge v\quad\text{for every column }j,\qquad
e_i^TAq\le v\quad\text{for every row }i,
$$
and $p^TAq=v$. These are the mutual best-response and security-level conditions.