TUGLab (version 0.0.1)

corevertices234: 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)

Value

If the core of v is non-empty, the core vertices are returned, as a matrix in which each row is a vertex.

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.

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 \(x(S)=\sum_{i\in S} x_i\).

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