drawNucleolus {CoopGame}

Draw nucleolus for 3 or 4 players

Description

drawNucleolus draws the nucleolus for 3 or 4 players.

Usage

drawNucleolus(v, holdOn = FALSE, colour = NA, label = TRUE, name = "Nucleolus")

Arguments

v

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

holdOn

draws in a existing plot

colour

draws the geometric object (i.e. point or convex polyhedron) with this colour, all colour names can be seen with "colors()"

label

activates the labels for the figure

name

set a name for the label

Value

None.

Author(s)

Johannes Anwander [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)
v=c(0,0,0,1,1,0,3)
drawNucleolus(v) 


#Visualization for 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)
drawNucleolus(v)