TUvalues (version 1.1.0)

centroid: Centroid of the core of the game

Description

Calculate the centroid of core of the game if it exits.

Usage

centroid(
  characteristic_func,
  n_players = 0,
  method = "exact",
  n_rep = 1000,
  echo = TRUE
)

Value

The centroid of the core if it exists.

Arguments

characteristic_func

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

n_players

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

method

Method used to calculate the core. Valid methods are: exact for the exact calculation or appro for approximated core based on Camacho et al. (2025).

n_rep

Only used if method is appro. The number of iterations to perform in the approximated calculation.

echo

Only used if method is appro. Show progress of the approximated calculation.

References

Camacho, J., Gonçalves-Dosantos, J. C., & Sánchez-Soriano, J. (2025). A Linear Programming Approach to Estimate the Core in Cooperative Games. arXiv preprint arXiv:2510.01766.

Examples

v <- c(2,3,5,5,7,8,10)
centroid(v, method = "exact")
centroid(v, method = "appro", n_rep = 100)

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)
 }
}
centroid(v, n, method = "exact")
centroid(v, n, method = "appro", n_rep = 200)