nucleolus: Compute nucleolus

In CoopGame: Important Concepts of Cooperative Game Theory

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 [e-mail]

Johannes Anwander [e-mail]

Daniel Gebele [e-mail]

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

CoopGame documentation built on Aug. 24, 2021, 1:07 a.m.