$(0,1)-$normalization of a cooperative game

Question

Let $v:2^{\{1,2,3\}}\to\mathbb{R}$ be a characteristic function game given by

$ v(S)=\left\{ \begin{array}{ll} -2 \qquad\text{ if $S$ has 1 member}\\ \ \ \ 2 \qquad\text{ if $S$ has 2 members}\\ \ \ \ 0 \qquad\text{ if $S$ has 3 members}\\ \end{array} \right. $

How do I compute its the strategically equivalent $(0,1)-$normalized game ? A game $v$ is $(0,1)-$normalized if $v(N)=1$ and $v(\{i\})=0.$

Answer 1

Use this formula:

$$\frac{v(S)-\sum_{i\in S}v(\{i\})}{v(N)-\sum_{i\in N}v(\{i\})}$$