shapleyValue: Compute Shapley value
In CoopGame: Important Concepts of Cooperative Game Theory

Description Usage Arguments Value Author(s) References Examples

Calculates the Shapley value for n players with formula from Lloyd Shapley.

1	shapleyValue(v)

`v`	Numeric vector of length 2^n - 1 representing the values of the coalitions of a TU game with n players

Shapley value for given game vector with n players

Alexandra Tiukkel

Jochen Staudacher jochen.staudacher@hs-kempten.de

Shapley L.S. (1953) "A value for n-person games". In: Kuhn, H., Tucker, A.W. (Eds.), Contributions to the Theory of Games II, Princeton University Press, pp. 307–317

Aumann R.J. (2010) "Some non-superadditive games, and their Shapley values, in the Talmud", Int. Journal of Game Theory 39(1), pp. 3–10

Peters H. (2015) Game Theory: A Multi-Leveled Approach, 2nd Edition, Springer, pp. 156–159

Maschler M., Solan E. and Zamir S. (2013) Game Theory, Cambridge University Press, pp. 748–781

Bertini C. (2011) "Shapley value", Encyclopedia of Power, SAGE Publications, p. 600–603

library(CoopGame)
shapleyValue(v=c(0,0,0,1,2,3,7.5))


#Example of a non-superadditive game,
#i.e. the inheritance problem due to Ibn Ezra (1146),
#from paper by Robert Aumann from 2010 on
#'Some non-superadditive games, and their Shapley values, in the Talmud'
library(CoopGame)
Aumann2010Example<-c(120,60,40,30,120,120,120,60,60,40,120,120,120,60,120)
shapleyValue(Aumann2010Example)
#[1] 80.83333 20.83333 10.83333  7.50000