= Solution
Transposing the second player's matrix leaves the row player's <security level payoff> at $12/5$. The column player's second action now yields payoffs $2$ and $3$, while its first yields zero for either row. Its <security level payoff> is therefore $2$, guaranteed by the second action; against the first row no mixture can guarantee more. Thus $d=(12/5,2)$.
The relevant upper <Pareto frontier> joins the payoff vectors $(4,2)$ and $(2,3)$, so $v=4-u/2$. On the segment satisfying <bargaining individual rationality> $12/5\leq u\leq4$, the <Nash product> becomes
$$
(u-12/5)(v-2)=(u-12/5)(2-u/2).
$$
Its <derivative> is $16/5-u$ and its second <derivative> is $-1$. Hence
$$
\boxed{N(F,d)=(16/5,12/5).}
$$
The implementing <correlated payoff lottery> chooses $(4,2)$ with probability $3/5$ and $(2,3)$ with probability $2/5$. Both players' gains are strictly positive: $4/5$ and $2/5$. The new <disagreement point> must be recomputed after transposition; reusing the previous column security payoff would solve a different <Nash bargaining problem>.
\Image[/past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2013/iii/paper-38-bargaining.png]
{title=Feasible payoff polygons, security points and Nash bargaining solutions before and after transposing the column payoff matrix}
{height=420}
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