strategicallyequivalentcheck {TUGLab} | R Documentation |
Strategically equivalent check
Description
This function checks if two games are strategically equivalent.
Usage
strategicallyequivalentcheck(v, w, binary = FALSE, parameters = FALSE)
Arguments
v |
A characteristic function, as a vector. |
w |
A characteristic function, as a vector. |
binary |
A logical value. By default, |
parameters |
A logical value. By default, |
Details
Games v\in G^N
and w\in G^N
are strategically equivalent if there exist k>0
and an additive game a\in G^N
such that v(S)=k w(S)+a(S)
for all S\in 2^N
.
Value
TRUE
if v
and w
are strategically equivalent, FALSE
otherwise. If parameters=TRUE
, whenever v
and w
are strategically equivalent, the function also returns k
(a positive integer) and a
(the characteristic function of an additive game, as a vector in binary order if binary=TRUE
and in lexicographic order otherwise) such that \code{v} = \code{k} \code{w} + \code{a}
.
See Also
additivegame, normalizedgame, zeronormalizedgame
Examples
w <- c(1000, 0, 0, 2000, 3000, 2000, 4000)
v <- 4.5 * w + additivegame(c(4, 6, 1), binary = TRUE)
strategicallyequivalentcheck(v, w, binary = TRUE, parameters = TRUE)