= Solution
For an $n$-player <transferable utility game> with $v(\varnothing)=0$, the <Shapley value> is
$$
\boxed{\phi_i(v)=\sum_{S\subseteq N\setminus\{i\}}\frac{|S|!\,(n-|S|-1)!}{n!}\left(v(S\cup\{i\})-v(S)\right).}
$$
It averages player $i$'s <marginal contribution> over uniformly random orders of all players. Exactly $|S|!(n-|S|-1)!$ of the $n!$ <permutations> put precisely $S$ before $i$. For a <cooperative cost game>, apply the same linear formula to the cost function; the result represents payments instead of distributed benefits.
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