isDegenerateGame {CoopGame}

Check if game is degenerate

Description

Checks if a TU game is degenerate. We call a game essential if the value of the grand coalition is greater than the sum of the values of the singleton coalitions. We call a game degenerate (or inessential), if

v(N) = \sum v({i})

.

Usage

isDegenerateGame(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 degenerate, else FALSE

Author(s)

Michael Maerz

Jochen Staudacher [e-mail]

Examples

library(CoopGame)
isDegenerateGame(c(1,2,3,4,4,4,6))


#The following game, i.e. the Maschler game, is not degenerate
library(CoopGame)
v1 <- c(0,0,0,60,60,60,72)
isDegenerateGame(v1) 

#The following game is also not degenerate
library(CoopGame)
v2 <- c(30,30,15,60,60,60,72)
isDegenerateGame(v2)

#The following game is degenerate
library(CoopGame)
v3 <- c(20,20,32,60,60,60,72)
isDegenerateGame(v3)