Description Usage Arguments Value Author(s) References Examples
View source: R/GameProperty1Convexity.R
is1ConvexGame checks if a TU game is 1-convex.
A TU game is 1-convex if and only if the following condition holds true:
Let S
be a nonempty coalition. Whenever all
players outside S
receive their payoffs according to the
utopia payoff of the game, then the remaining part of the total savings
is at least v(S)
.
1 |
v |
Numeric vector of length 2^n - 1 representing the values of the coalitions of a TU game with n players |
TRUE
if the game is 1-convex, else FALSE
Jochen Staudacher jochen.staudacher@hs-kempten.de
Driessen T. (1998) Cooperative Games, Solutions and Applications, Springer, p. 73
1 2 3 4 5 6 7 8 9 10 11 12 13 | library(CoopGame)
is1ConvexGame(c(0,0,0,9,9,12,18))
#1-convex game (taken from book by T. Driessen, p. 75)
library(CoopGame)
v=c(0,0,0,9,9,15,18)
is1ConvexGame(v)
#Example of a game which is not 1-convex
library(CoopGame)
v=c(1:7)
is1ConvexGame(v)
|
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