TUGLab (version 0.0.1)

coredimension: Core dimension

Description

Given a game, this function computes the dimension of its core.

Usage

coredimension(v, binary = FALSE, tol = 1e-12)

Value

The dimension of the core of v, as an integer.

Arguments

v

A characteristic function, as a vector.

binary

A logical value. By default, binary=FALSE. Should be set to TRUE if v is introduced in binary order instead of lexicographic order.

tol

A tolerance parameter, as a non-negative number.
By default, tol=100*.Machine$double.eps.

Details

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

References

Edgeworth, F. Y. (1881). Mathematical psychics: An essay on the application of mathematics to the moral sciences. CK Paul.

Gillies, D. (1953). Some theorems on n-person games. PhD thesis, Princeton, University Press Princeton, New Jersey.

See Also

balancedcheck, corevertices, corevertices234, plotcoreset, plotcoresets

Examples

v1 <- c(rep(0,5),rep(1,4),0,rep(1,3),2,2)
plotcoreset(v1)
coredimension(v1)

v2 <- c(rep(0,5),rep(1,4),0,rep(1,4),2)
plotcoreset(v2)
coredimension(v2)

v3 <- marginalgame(c(0,0,0,0,0,0,0,0,1,4,1,3,6,8,10),1)
plotcoreset(v3)
coredimension(v3)

v4 <- c(0,0,0,0,0,0,0,0,1,4,1,3,6,8,10)
plotcoreset(v4)
coredimension(v4)