= Solution
The dual is
$$
\boxed{D:\ \min_{y\ge0}\mathbf1^\mathsf Ty\quad\text{subject to }A^\mathsf Ty\ge\mathbf1.}
$$
For positive payoffs and an optimal solution $y_*$, <strong duality> gives $\mathbf1^\mathsf Ty_*=1/v$. Normalizing gives Player I's optimal row strategy $p_*=y_*/(\mathbf1^\mathsf Ty_*)$. Its expected payoff against every column is at least $v$. Thus the primal represents Player II's minimization of worst loss and the dual represents Player I's maximization of guaranteed gain.
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