Shapley value

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

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 ${\displaystyle v\;:\;{\mathcal {P}}(N)\;\to \Re }$.