isQuasiBalancedGame {CoopGame}

Check if game is quasi-balanced

Description

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.

Usage

isQuasiBalancedGame(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 quasi-balanced, else FALSE.

Author(s)

Johannes Anwander [e-mail]

Jochen Staudacher [e-mail]

References

Branzei R., Dimitrov D. and Tijs S. (2006) Models in cooperative game theory, Springer, p. 31

Examples

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)