isConvexGame {CoopGame}

Check if game is convex

Description

isConvexGame checks if a TU game is convex. A TU game is convex if and only if each player's marginal contribution to any coalition is monotone nondecreasing with respect to set-theoretic inclusion.

Usage

isConvexGame(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 convex, 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. 10

Peters H. (2015) Game Theory: A Multi-Leveled Approach, 2nd Edition, Springer, p. 329

Maschler M., Solan E. and Zamir S. (2013) Game Theory, Cambridge University Press, pp. 717–718

Osborne M.J. and Rubinstein A. (1994) A Course in Game Theory, MIT Press, pp. 260–261

Examples

library(CoopGame)
isConvexGame(c(0,0,0,1,1,1,5))


#Example of a convex game with three players
library(CoopGame) 
v=c(0,0,0,1,2,1,4)
isConvexGame(v)

#Example of a nonconvex game
library(CoopGame) 
v=c(1:7)
isConvexGame(v)