Noun
Shapley value
(game theory) A real number determined for the player i as
ϕ
i
(
v
)
=
∑
S
⊆
N
∖
{
i
}
|
S
|
!
(
n
−
|
S
|
−
1
)
!
n
!
(
v
(
S
∪
{
i
}
)
−
v
(
S
)
)
{\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
v
:
P
(
N
)
→
ℜ
{\displaystyle v\;:\;{\mathcal {P}}(N)\;\to \Re }
.