iskConvexGame {CoopGame}

Check if game is k-Convex

Description

iskConvexGame checks if a TU game is k-convex. A TU game is k-convex if and only if its k-cover exists and is convex. See section 7.1 of the book by Driessen for more details

Usage

iskConvexGame(v, k)

Arguments

v

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

k

An integer specifying k

Value

TRUE if the game is k-convex, else FALSE

Author(s)

Jochen Staudacher [e-mail]

References

Driessen T. (1998) Cooperative Games, Solutions and Applications, Springer, p. 171–178

Examples

library(CoopGame)
iskConvexGame(v=c(0,0,0,9,9,12,18), k=1)


# Two examples motivated by the book by T. Driessen, p. 175:
#
# The following game is 2-convex 
library(CoopGame)
alpha = 0.4
v=c(0,0,0,alpha,alpha,0,1)
iskConvexGame(v,2)

# The following game is not 2-convex 
library(CoopGame)
alpha = 0.7
v=c(0,0,0,alpha,alpha,0,1)
iskConvexGame(v,2)