| nucleolus {CoopGame} | R Documentation |
Compute nucleolus
Description
Computes the nucleolus of a TU game with a non-empty imputation set and n players. Note that the nucleolus is a member of the imputation set.
Usage
nucleolus(v)
Arguments
v |
Numeric vector of length 2^n - 1 representing the values of the coalitions of a TU game with n players |
Value
Numeric vector of length n representing the nucleolus.
Author(s)
Jochen Staudacher jochen.staudacher@hs-kempten.de
Johannes Anwander anwander.johannes@gmail.com
Daniel Gebele daniel.a.gebele@stud.hs-kempten.de
References
Schmeidler D. (1969) "The nucleolus of a characteristic function game", SIAM Journal on applied mathematics 17(6), pp. 1163–1170
Kohlberg E. (1971) "On the nucleolus of a characteristic function game", SIAM Journal on applied mathematics 20(1), pp. 62–66
Kopelowitz A. (1967) "Computation of the kernels of simple games and the nucleolus of n-person games", Technical Report, Department of Mathematics, The Hebrew University of Jerusalem, 45 pages.
Megiddo N. (1974) "On the nonmonotonicity of the bargaining set, the kernel and the nucleolus of a game", SIAM Journal on applied mathematics 27(2), pp. 355–358
Peleg B. and Sudhoelter P. (2007) Theory of cooperative games, 2nd Edition, Springer, pp. 82–86
Examples
library(CoopGame)
nucleolus(c(1, 1, 1, 2, 3, 4, 5))
library(CoopGame)
nucleolus(c(0, 0, 0, 0, 5, 5, 8, 9, 10, 8, 13, 15, 16, 17, 21))
#[1] 3.5 4.5 5.5 7.5
#Final example:
#Estate division problem from Babylonian Talmud with E=300,
#see e.g. seminal paper by Aumann & Maschler from 1985 on
#'Game Theoretic Analysis of a Bankruptcy Problem from the Talmud'
library(CoopGame)
v<-bankruptcyGameVector(n=3,d=c(100,200,300),E=300)
nucleolus(v)
#[1] 50 100 150