isMonotonicGame {CoopGame}

Check if game is monotonic

Description

Checks if a TU game with n players is monotonic.
For a monotonic game a coalition S can never obtain a larger value than another coalition T if S is contained in T.

Usage

isMonotonicGame(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 monotonic, else FALSE

Author(s)

Johannes Anwander [e-mail]

Jochen Staudacher [e-mail]

References

Peleg B. and Sudhoelter P. (2007) Theory of cooperative games, 2nd Edition, Springer, p. 12

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

Examples

library(CoopGame)
isMonotonicGame(c(0,0,0,1,0,1,1))


#Example of a non-monotonic game
library(CoopGame)
v1=c(4,2,5,2,3,6,10)
isMonotonicGame(v1)

#Example of a monotonic game
library(CoopGame)
v2=c(2,5,7,10, 9, 13,20)
isMonotonicGame(v2)