CoopGame (version 0.2.2)

isConvexGame: 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

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

# NOT RUN {
library(CoopGame)
isConvexGame(c(0,0,0,1,1,1,5))

# }
# NOT RUN {
#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)
# }
# NOT RUN {
# }