# Shapley value

## English

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### Noun

1. (game theory) A real number determined for the player i as
$\phi_i(v)=\sum_{S \subseteq N \setminus \{i\}} \frac{|S|!\; (n-|S|-1)!}{n!}(v(S\cup\{i\})-v(S))$,
given a coalitional game with a set N of n players and a worth function $v \; : \; \mathcal{P}(N) \; \to \Re$.