Another (quick) question;
Let $T \subset N$ be a coalition. The unanimity game on $T$ is the game $(N, u_T)$ where $u_T(S)=1$ if $T \subset S$ and $u_T(S)=0$ if $T\S$. In other words, a coalition $S$ has worth $1$ (is winning) if it contains all players of $T$, and worth $0$ (is loosing) if this is not the case.
Calculate the core and the Shapley value for $(N, u_T)$
Then the core consists of $x_n-m \geq 0$ with $m \in [0,n-1]$
And then we know $x_n - 0 + x_n - 1 + \dots + xn - (n-1) = 1$ (efficiency)
So we could denote the core as $x_n - m + x_n - m' \geq 0$ + the efficiency
Am I right thinking the Shapley value should be
\begin{array}{|1|} \hline \frac{1}{n-1!} \cdot (\frac{1}{n},\frac{1}{n},\dots,\frac{1}{n})=(\frac{1}{n!},\frac{1}{n!},\dots,\frac{1}{n!}) \\\tag{1} \hline \end{array}
Is this ok? Thanks!