TUGLab (version 0.0.1)

dummynull: Dummy and null players

Description

Given a game, this function identifies its dummy players and null players.

Usage

dummynull(v, binary = FALSE, tol = 100 * .Machine$double.eps)

Value

Two different vectors are returned: one containing the dummy players and the other containing the null players.

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.

tol

A tolerance parameter, as a non-negative number.
By default, tol=100*.Machine$double.eps.

Details

Given a game \(v\in G^N\), \(i \in N\) is said to be a dummy player if \(v(S) + v(\{i\}) = v(S \cup \{i\})\) for all \(S \subset N \setminus \{i\}\).

A dummy player \(i \in N\) is said to be a null player if \(v(\{i\})=0\).

Examples

v <- c(0,1,0,1,0,1,1)
dummynull(v)
# Checking if a particular player is a dummy player:
2 %in% dummynull(v)$dummy # player 2 is a dummy player in v
2 %in% dummynull(v)$null # player 2 is not a null player in v