dummynull {TUGLab}R Documentation

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)

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.

Value

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

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

[Package TUGLab version 0.0.1 Index]