Past exam of the mathematics course of the University of Cambridge / 2001 / iii / Paper 31 / 6 / a / Solution

For a transferable utility game, an imputation is an efficient and individually rational payoff allocation:Here it isWriting $z_1=x_1-1$, $z_2=x_2-2$, $z_3=x_3-3$ 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 $(1,2,9)$.