Solution
= Solution
For a <transferable utility game>, an <imputation> is an efficient and individually rational <payoff> allocation:
$$
I(v)=\left\{x\in\mathbb R^3:\sum_i x_i=v(N),\quad x_i\ge v(\{i\})\right\}.
$$
Here it is
$$
\boxed{I(v)=\{x:x_1+x_2+x_3=12,\ x_1\ge1,\ x_2\ge2,\ x_3\ge3\}.}
$$
Writing $z_1=x_1-1$, $z_2=x_2-2$, $z_3=x_3-3$ identifies it with a scaled <standard simplex> $z_1+z_2+z_3=6$. Its three vertices are $(7,2,3)$, $(1,8,3)$ and $(1,2,9)$.