= Shapley value
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{title2=$\phi_i(v)=\sum_{S\subseteq N\setminus\{i\}}\frac{|S|!(n-|S|-1)!}{n!}\bigl(v(S\cup\{i\})-v(S)\bigr)$}
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The <Shapley value> averages each player's <marginal contribution> over uniformly random player orderings. Exactly $|S|!(n-|S|-1)!$ orderings have $S$ immediately before player $i$, giving the formula. The values sum to $v(N)$ by telescoping each ordering. In a <simple cooperative game> this is the <probability> of being pivotal. For a <convex cooperative game>, <Shapley value belongs to the core of a convex game> guarantees a stable allocation as well.
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