TUGLab (version 0.0.1)

plotcoresets: Plot multiple core sets

Description

Given multiple games with two, three or four players, this function draws in a single plot their projected core sets and sets of imputations.

Usage

plotcoresets(games, binary = FALSE, imputations = TRUE)

Value

A plot of the given core sets.

Arguments

games

A matrix in which each row is a characteristic function.

binary

A logical value. By default, binary=FALSE. Should be set to TRUE if the characteristic functions in games are introduced in binary order instead of lexicographic order.

imputations

A logical value. By default, imputations=TRUE. When set to imputations=FALSE, the sets of imputations are not drawn.

Details

The core of a game $v\in G^N$ is the set of all its stable imputations: $$C(v)=\{x\in {\mathbb{R}}^n:x(N)=v(N),x(S)\ge v(S)\mathrm{\forall }S\in 2^N\},$$ where $x(S)=\sum _{i\in S}{x}_i$.

See Also

plotcoreset

Examples

# Plotting the core and the least core of a game:
v <- c(0,0,0,0,10,40,30,60,10,20,90,90,90,130,160)
vt <- leastcore(v)$vt
plotcoresets(games = rbind(v,vt), imputations = FALSE)