= Solution
{c}
For the minimizing player, column one weakly dominates column three, since its payoff is no greater in every row. We may therefore choose an optimum with $q_3=0$. Write $q=(x,1-x,0)$, $0\leq x\leq1$. The three row payoffs are $6-5x$, $5-3x$, and $1+2x$.
The maximum of the decreasing line $5-3x$ and the increasing line $1+2x$ is minimized where they meet: $x=4/5$, with value $13/5$. At this point the first line is only $2$, so it does not increase the maximum. Hence the candidate is
$$
\boxed{q_*=(4/5,1/5,0),\qquad v=13/5.}
$$
A dual certificate establishes optimality against every possible three-column mixture. Player I's strategy $p_*=(0,2/5,3/5)$ gives column payoffs $(13/5,13/5,16/5)$, guaranteeing at least $13/5$. The displayed $q_*$ holds every row payoff to at most $13/5$. These matching guarantees prove the claimed value and optimality.
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