isSuperadditiveGame {CoopGame}

Check if game is superadditive

Description

Checks if a TU game with n players is superadditive.
In a superadditive game for any two disjoint coalitions S and T the value of the union of S and T is always greater or equal the sum of the values of S and T. In other words, the members of any two disjoint coalitions S and T will never be discouraged from collaborating.

Usage

isSuperadditiveGame(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 superadditive, else FALSE.

Author(s)

Alexandra Tiukkel

Jochen Staudacher [e-mail]

References

Peleg B. and Sudhoelter P. (2007) Theory of cooperative games, 2nd Edition, Springer, p. 10

Peters H. (2015) Game Theory: A Multi-Leveled Approach, 2nd Edition, Springer, p. 295

Maschler M., Solan E. and Zamir S. (2013) Game Theory, Cambridge University Press, p. 671

Narahari Y. (2015) Game Theory and Mechanism Design, World Scientific Publishing, p. 408

Examples

library(CoopGame)
isSuperadditiveGame(c(0,0,0,1,1,1,2))


#Example of a superadditive game
library(CoopGame)
v1=c(0,0,0,40,50,20,100) 
isSuperadditiveGame(v1)

#Example of a game that is not superadditive 
library(CoopGame)
v2=c(0,0,0,40,30,130,100) 
isSuperadditiveGame(v2)

#Another example of a superadditive game
library(CoopGame)
v3=c(1,1,1,1, 2,2,2,2,2,2, 3,3,3,3, 4)
isSuperadditiveGame(v3)