constantsumgame {TUGLab} | R Documentation |
Constant sum game
Description
This function computes the characteristic function of the specified constant sum game.
Usage
constantsumgame(halfv, vN)
Arguments
halfv |
The first half (according to lexicographic or binary order) of the characteristic function (excluding the grand coalition), as a vector. |
vN |
The utility of the grand coalition. |
Details
A game v\in G^N
is a constant sum game if, for each S \in 2^{N}
,
v(S) + v(N \setminus S) = v(N)
. Thus, if v
is a constant sum game and F
is
a family of 2^{n-1}-1
coalitions such that S \cup T \neq N
for any S,T \in F
,
the full characteristic function of v
is strictly determined by the utilities of
the coalitions in F
and the utility of the grand coalition.
Value
The characteristic function of the constant sum game. It is to be interpreted according to the order that halfv
is introduced in.
Examples
constantsumgame(c(0,0,0), 1) # the dollar game
# Building a random constant sum game:
players <- sample(3:6,1) # random number of players between three and six
halfv <- runif(2^(players-1)-1, 0, 10) # random halfv
vN <- runif(1,30,50) # random vN
constantsumgame(halfv, vN)
[Package TUGLab version 0.0.1 Index]