isSemiConvexGame {CoopGame}

Check if game is semiconvex

Description

isSemiConvexGame checks if a TU game is semiconvex. A TU game is semiconvex if and only if the following conditions hold true: The gap function of any single player i is minimal among the gap function values of coalitions S containing player i. Also, the gap function itself is required to be nonnegative.

Usage

isSemiConvexGame(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 semiconvex, else FALSE.

Author(s)

Jochen Staudacher [e-mail]

References

Driessen T. and Tijs S. (1985) "The tau-value, the core and semiconvex games", Int. Journal of Game Theory 14(4), pp. 229–247

Driessen T. (1998) Cooperative Games, Solutions and Applications, Springer, p. 76

Examples

library(CoopGame)
isSemiConvexGame(c(0,0,0,1,1,1,4))


#Example of a semiconvex game 
library(CoopGame)
v1<-c(3,4,5,9,10,11,18)
isSemiConvexGame(v1)

#Example of a game which not semiconvex 
library(CoopGame)
v2=c(1:7)
isSemiConvexGame(v2)