owen: Owen value

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

Owen value

Description

Calculate the Owen value

Usage

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

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.
method	Method used to calculate the Owen value. Valid methods are: exact for the exact calculation or appro for approximated polynomial calculation based on sampling proposed by Saavedra-Nieves et al. (2018).
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.

Value

The Owen value for each player.

References

Saavedra-Nieves, A., García-Jurado, I., & Fiestras-Janeiro, M. G. (2018). Estimation of the Owen value based on sampling. In The mathematics of the uncertain: A tribute to Pedro Gil (pp. 347-356). Cham: Springer International Publishing.

Examples

n <- 10
v <- function(coalition) {
  if (length(coalition) > n/2) {
    return(1)
  } else {
    return(0)
  }
}
u <- lapply(1:(n/2), function(i) c(2*i - 1, 2*i))
owen(v, union = u, method = "appro", n_rep = 4000, n_players = n)

characteristic_func <- c(1,1,2,1,2,2,2)
union <- list(c(1,2),c(3))
owen(characteristic_func, union)
owen(characteristic_func, union, method = "appro", n_rep = 4000)

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