TUvalues (version 1.1.0)

equal_surplus_division_unions: Equal Surplus Division value with a priori unions

Description

Calculate the equal surplus division value in games with a priori unions

Usage

equal_surplus_division_unions(
  characteristic_func,
  union,
  n_players = 0,
  type = 1
)

Value

The equal surplus division value for each player

Arguments

characteristic_func

The valued function defined on the subsets of the number of players

union

List of vectors indicating the a priori unions between the players.

n_players

Only used if characteristic_func is a function. The number of players in the game.

type

Number indicating the type of equal surplus division value to compute following Alonso-Meijide et al. (2020). Values 1, 2 and 3 are implemented.

References

Alonso-Meijide, J. M., Costa, J., García-Jurado, I., & Gonçalves-Dosantos, J. C. (2020). On egalitarian values for cooperative games with a priori unions. Top, 28(3), 672-688.

Examples

n <- 3
v <- function(coalition) {
 size <- length(coalition)
 if (size <= 1) {
   return(0)
 } else if (size == 2) {
   return(10)
 } else if (size == 3) {
   return(24)
 } else {
   return(0)
 }
}
union <- list(1:4,5:n)
equal_surplus_division_unions(v,union,n,type = 1)

v <- c(1,1,2,1,2,2,2)
union <- list(c(1,2),c(3))
equal_surplus_division_unions(v, union, type = 2)