isBalancedGame {CoopGame} | R Documentation |
Checks if a game is balanced. A game is balanced if the core is a nonempty set.
isBalancedGame(v)
v |
Numeric vector of length 2^n - 1 representing the values of the coalitions of a TU game with n players |
TRUE
if the game is balanced, else FALSE
Jochen Staudacher jochen.staudacher@hs-kempten.de
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
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)