Shapley value

Shapley value

English

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

Translations

payoff of a player

Czech: Shapleyho hodnota f