I'm reading the original Shapley values paper, page 70, which was published in 1953. In this paper Shapley writes the following:
where $U$ is the "universe of all players" that can take part in a game, in other words, the set of all players. From the description, I think $\Pi(U)$ is meant to denote the powerset of $U$, $\mathcal P(U)$, and $\Pi$ is an old out-of-use notation. Can anybody confirm?
No. The powerset $\mathcal P(U)$ is the set of subsets of $U$. The permutations of $U$ are different objects.
For an example, $$\mathcal P(\{1,2\})=\big\{\emptyset,\{1\},\{2\},\{1,2\}\big\}$$ consists of the $2^2=4$ subsets of $\{1,2\}$, while $$\Pi(\{1,2\})=\big\{(12),(21)\big\},$$ where $(12)$ denotes the function sending $1\to 1$ and $2\to 2$, while $(21)$ denotes the function sending $2\to 1$ and $1\to 2$. In general, if $U$ is a finite set of size $n$, then $\mathcal P(U)$ has $2^n$ elements, while $\Pi(U)$ has $n!$ elements.