| isBalancedGame {CoopGame} | R Documentation |
Check if game is balanced
Description
Checks if a game is balanced. A game is balanced if the core is a nonempty set.
Usage
isBalancedGame(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 balanced, else FALSE
Author(s)
Jochen Staudacher jochen.staudacher@hs-kempten.de
References
Bondareva O.N. (1963) "Some applications of linear programming methods to the theory of cooperative games". Problemy kibernetiki 10, pp. 119–139
Shapley L.S. (1967) "On Balanced Sets and Cores". Naval Research Logistics Quarterly 14, pp. 453–460
Peleg B. and Sudhoelter P. (2007) Theory of cooperative games, 2nd Edition, Springer, pp. 27–32
Maschler M., Solan E. and Zamir S. (2013) Game Theory, Cambridge University Press, pp. 691–702
Slikker M. and van den Nouweland A. (2001) Social and Economic Networks in Cooperative Game Theory, Springer, pp. 6–7
Osborne M.J. and Rubinstein A. (1994) A Course in Game Theory, MIT Press, pp. 262–263
Examples
library(CoopGame)
v=c(0,0,0,40,50,20,100)
isBalancedGame(v)
#Example of an unbalanced game with 3 players
library(CoopGame)
v=c(1,1,1,2,3,4,3)
isBalancedGame(v)
#Example of an unbalanced game with 4 players
library(CoopGame)
v=c(0,0,0,0,1,0,0,0,0,3,3,3,3,3,4)
isBalancedGame(v)
#Example of a balanced game with 4 players
library(CoopGame)
v= c(0,0,0,0,1,0,0,0,0,2,2,2,2,2,4)
isBalancedGame(v)