TUvalues (version 1.1.1)

owen: Owen value

Description

Calculate the Owen value

Usage

owen(
  characteristic_func,
  union,
  n_players = 0,
  method = "exact",
  n_rep = 10000,
  echo = TRUE
)

Value

The Owen 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

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.

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)