coredimension {TUGLab} | R Documentation |
Core dimension
Description
Given a game, this function computes the dimension of its core.
Usage
coredimension(v, binary = FALSE, tol = 1e-12)
Arguments
v |
A characteristic function, as a vector. |
binary |
A logical value. By default, |
tol |
A tolerance parameter, as a non-negative number. |
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
.
Value
The dimension of the core of v
, as an integer.
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)