| shapleyValue {CoopGame} | R Documentation |
Compute Shapley value
Description
Calculates the Shapley value for n players with formula from Lloyd Shapley.
Usage
shapleyValue(v)
Arguments
v |
Numeric vector of length 2^n - 1 representing the values of the coalitions of a TU game with n players |
Value
Shapley value for given game vector with n players
Author(s)
Alexandra Tiukkel
Jochen Staudacher jochen.staudacher@hs-kempten.de
References
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
Examples
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