corevertices {TUGLab} | R Documentation |
Core vertices
Description
Given a game, this function computes its core vertices.
Usage
corevertices(v, binary = FALSE)
Arguments
v |
A characteristic function, as a vector. |
binary |
A logical value. By default, |
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
If the core of v
is non-empty, the core vertices are returned, as a matrix in which each row is a vertex.
Note
Function corevertices234
can also compute the core vertices of games with less than five players, but takes a different approach.
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, corevertices234, plotcoreset, plotcoresets
Examples
v=c(0,0,0,0,0,0,0,0,1,4,1,3,6,8,10)
corevertices(v)
# What if the game is a cost game?
cost.v <- c(2,2,2,3,4,4,5) # cost game
-corevertices(-cost.v) # core vertices of the cost game