shapleyvalue {TUGLab}R Documentation

Shapley value

Description

Given a game, this function computes its Shapley value.

Usage

shapleyvalue(v, binary = FALSE)

Arguments

v

A characteristic function, as a vector.

binary

A logical value. By default, binary=FALSE. Should be set to TRUE if v is introduced in binary order instead of lexicographic order.

Details

Given v\in G^N, the Shapley value of each player i \in N can be defined as

Sh_{i}(v) = \sum_{S \subset N \setminus \{i\}} \frac{s!(n-s-1)!}{n!} (v(S \cup \{i\})-v(S)).

It is also possible to compute it as

Sh_{i}(v) = \sum_{\emptyset \neq S \subset N} M_{i,S} v(S),

where M_{i,S} = \frac{(s-1)!(n-s)!}{n!} if i \in S and M_{i,S} = -\frac{s!(n-s-1)!}{n!} if i \notin S.

Value

The Shapley value of the game, as a vector.

References

Le Creurer, I. J., Mirás Calvo, M. A., Núñez Lugilde, I., Quinteiro Sandomingo, C., & Sánchez Rodríguez, E. (2024). On the computation of the Shapley value and the random arrival rule. Available at https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4293746.

Shapley, L. S. (1953). A value for n-person games. Contribution to the Theory of Games, 2.

See Also

marginalvector

Examples

shapleyvalue(c(0,0,3,0,3,8,6,0,6,9,15,8,16,17,20), binary=TRUE)
shapleyvalue(claimsgame(E=69.420,d=runif(10,5,10)))

[Package TUGLab version 0.0.1 Index]