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$double.eps)
Arguments
v |
A characteristic function, as a vector. |
binary |
A logical value. By default, |
tol |
A tolerance parameter, as a non-negative number. |
Details
Given a game v\in G^N
, i \in N
is said to be a dummy player
if v(S) + v(\{i\}) = v(S \cup \{i\})
for all S \subset N \setminus \{i\}
.
A dummy player i \in N
is said to be a null player if v(\{i\})=0
.
Value
Two different vectors are returned: one containing the dummy players and the other containing the null players.
Examples
v <- c(0,1,0,1,0,1,1)
dummynull(v)
# Checking if a particular player is a dummy player:
2 %in% dummynull(v)$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]