is1ConvexGame {CoopGame}

Check if game is 1-Convex

Description

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).

Usage

is1ConvexGame(v)

Arguments

v

Numeric vector of length 2^n - 1 representing the values of the coalitions of a TU game with n players

Value

TRUE if the game is 1-convex, else FALSE

Author(s)

Jochen Staudacher [e-mail]

References

Driessen T. (1998) Cooperative Games, Solutions and Applications, Springer, p. 73

Examples

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)