symmetrycheck {TUGLab}R Documentation

Symmetry check

Description

Given a game and two players, this function checks if those are symmetric players.

Usage

symmetrycheck(v, i, j, binary = FALSE, tol = 100 * .Machine$double.eps)

Arguments

v

A characteristic function, as a vector.

i

The position of an individual coalition, as an integer.

j

The position of another individual coalition, as an integer.

binary

A logical value. By default, binary=FALSE. Should be set to TRUE if v, i and j are 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

Let v\in G^N. Players i,j \in N are symmetric in v if, for each S \subset N with i,j \in S, v(S \setminus \{i\}) = v(S \setminus \{j\}).

Value

TRUE if i and j are symmetric in v, FALSE otherwise.

Examples

symmetrycheck(c(13,13,0,0,58,58,0),1,2) # players 1 and 2 are symmetric

[Package TUGLab version 0.0.1 Index]