corevertices234 {TUGLab} | R Documentation |
Core vertices of games with two, three or four players
Description
Given a game with no more than four players, this function computes its core vertices.
Usage
corevertices234(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 corevertices
can also compute the core vertices of games with less than five players, but takes a different approach.
See Also
balancedcheck, corevertices, plotcoreset,
Examples
# 2 players:
corevertices234(c(-58,4,13))
# 3 players:
corevertices234(c(1,5,10,6,11,15,16)) # additive game
# 4 players:
corevertices234(c(0,0,0,0,4,3,5,2,4,5,10,19,20,30,100)) # convex game
corevertices234(c(0,0,0,0,1,2,1,1,1,1,4,3,2,1,7)) # not convex game
# What if the game is a cost game?
cost.v <- c(2,2,2,3,4,4,5) # cost game
-corevertices234(-cost.v) # core vertices of the cost game
[Package TUGLab version 0.0.1 Index]