= Solution
A <security level payoff> maximizes what a player guarantees against the opponent. Let $p$ be the row player's probability of the first action. Its guaranteed payoff is
$$
\min\{3-3p,2+2p\}.
$$
The decreasing and increasing terms cross at $p=1/5$, attaining $d_1=12/5$; moving either way lowers the smaller term. For the column player, any mixture has zero payoff against the first row, while its second-row payoff is nonnegative. Therefore $d_2=0$ and
$$
d=(12/5,0).
$$
The feasible set is the <convex hull> of the four joint pure-action payoff vectors. Its upper <Pareto frontier> connects $(4,0)$ to $(3,2)$ to $(2,3)$. Write the row payoff as $u$ and column payoff as $v$. On the first <Pareto frontier> segment, $v=8-2u$ for $3\leq u\leq4$. The <Nash product> is
$$
(u-12/5)(8-2u),
$$
a concave quadratic with <derivative> $64/5-4u$, maximized at $u=16/5$, $v=8/5$, giving product $32/25$. On the portion of the other <Pareto frontier> segment satisfying <bargaining individual rationality>, $12/5\leq u\leq3$ and $v=5-u$. Its product <derivative> $37/5-2u$ is positive throughout, so its largest product is $6/5$ at $(3,2)$, smaller than $32/25$. All dominated points can be discarded by <Pareto efficiency>. Consequently
$$
\boxed{N(F,d)=(16/5,8/5).}
$$
This payoff is implemented by a <correlated payoff lottery> choosing the payoff $(4,0)$ with probability $1/5$ and $(3,2)$ with probability $4/5$. The <convex hull> permits such lotteries over joint outcomes; it is not restricted to independent <mixed strategies>.
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