equal_surplus_division_unions: Equal Surplus Division value with a priori unions

In TUvalues: Tools for Calculating Allocations in Game Theory using Exact and Approximated Methods

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
)

Arguments

characteristic_func	The characteristic function of the game. It can be a numeric vector with the value of every coalition, in the order given by coalitions: of length 2^n - 1, without the empty coalition (whose value is taken as 0), or of length 2^n, with the empty coalition first. Vectors support up to 30 players. It can also be a function that receives a coalition (a vector of players) and returns its value; in that case there is no limit on 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.

Value

The equal surplus division value for each player

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(1:2,3)
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)

TUvalues documentation built on Nov. 8, 2026, 1:19 a.m.