isQuasiBalancedGame {CoopGame} | R Documentation |
Checks if a TU game is quasi-balanced.
A TU game is quasi-balanced if
a) the components of its minimal rights vector are
less or equal than the components of its utopia payoff
vector
and
b) the sum of the components of its minimal rights vector
is less or equal the value of the grand coalition which
in turn is less or equal than the sum of the components
of its utopia payoff vector.
Note that any balanced game is also quasi-balanced,
but not vice versa.
Note that the quasi-balanced games are those games with
a non-empty core cover.
Note also that quasi-balancedness is sometimes in the
literature also referred to as compromise-admissibility.
isQuasiBalancedGame(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 quasi-balanced, else FALSE
.
Johannes Anwander anwander.johannes@gmail.com
Jochen Staudacher jochen.staudacher@hs-kempten.de
Branzei R., Dimitrov D. and Tijs S. (2006) Models in cooperative game theory, Springer, p. 31
library(CoopGame) isQuasiBalancedGame(c(0,0,0,1,1,1,4)) #Example of a quasi-balanced game: library(CoopGame) v1=c(1,1,2,6,8,14,16) isQuasiBalancedGame(v1) #Example of a game which is not quasi-balanced: library(CoopGame) v2=c(1:7) isQuasiBalancedGame(v2)