totallybalancedcheck {TUGLab} | R Documentation |
Totally balanced check
Description
This function checks if the given game is totally balanced and computes its totally balanced cover.
Usage
totallybalancedcheck(
v,
game = FALSE,
binary = FALSE,
tol = 100 * .Machine$double.eps
)
Arguments
v |
A characteristic function, as a vector. |
game |
A logical value. By default, |
binary |
A logical value. By default, |
tol |
A tolerance parameter, as a non-negative number. |
Details
A game v \in G^{N}
is totally balanced if all of its subgames are balanced
(the subgame of each coalition S \in 2^{N}
with respect to v
is defined by
v_S(T)=v(T)
for all T\in 2^S
).
Value
TRUE
if the game is totally balanced, FALSE
otherwise. If game=TRUE
, the totally balanced cover of the game is also returned.
References
Maschler, M., Solan, E., & Zamir, S. (2013). Game Theory. Cambridge University Press.
See Also
Examples
totallybalancedcheck(c(0,0,0,0,1/2,0,0,1/2,0,1/2,1/2,1/2,1/2,1/2,1))
totallybalancedcheck(c(0,0,0,0,1,1,0,1,0,0,1,1,1,1,2),game=TRUE)