Solution (source code)

= Solution
{c}

Player I can choose each row with <probability> $1/m$. Against column $j$ the expected payoff is $m^{-1}\sum_i a_{ij}$. Nonnegativity and a strictly positive entry in each column make every one of these finitely many numbers strictly positive. Their minimum
$$
\delta=\min_j\frac1m\sum_i a_{ij}>0
$$
is therefore a guaranteed payoff against every mixture of columns. By the <minimax theorem>, \b[$v\geq\delta>0$].