# Shapley value

## English

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### Etymology

Named in honour of Lloyd Shapley, who introduced it in 1953.

### Noun

Shapley value

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