Type:	Package
Title:	Tools for Calculating Allocations in Game Theory using Exact and Approximated Methods
Version:	1.0.0
Description:	The main objective of cooperative games is to allocate a good among the agents involved. This package includes the most well-known allocation rules, i.e., the Shapley value, the Banzhaf value, the egalitarian rule, and the equal surplus division value. In addition, it considers the point of view of a priori unions (situations in which agents can form coalitions). For this purpose, the package includes the Owen value, the Banzhaf-Owen value, and the corresponding extensions of the egalitarian rules. All these values can be calculated exactly or estimated by sampling.
License:	AGPL (≥ 3)
Encoding:	UTF-8
RoxygenNote:	7.3.2
URL:	https://github.com/mariaguilleng/TUvalues
BugReports:	https://github.com/mariaguilleng/TUvalues/issues
Imports:	utils, gtools
NeedsCompilation:	no
Packaged:	2025-05-22 16:46:45 UTC; meryg
Author:	Maria D. Guillen [cre, aut], Juan Carlos Gonçalves [aut]
Maintainer:	Maria D. Guillen <maria.guilleng@umh.es>
Repository:	CRAN
Date/Publication:	2025-05-22 17:10:02 UTC

Banzhaf value

Description

Calculate the Banzhaf value

Usage

banzhaf(
  characteristic_func,
  method = "exact",
  n_rep = 10000,
  n_players = 0,
  replace = FALSE
)

Arguments

Value

The Banzhaf value for each player

Examples

n <- 8
v <- function(coalition) {
if (length(coalition) > n/2) {
   return(1)
 } else {
   return(0)
 }
}
banzhaf(v, method = "exact", n_players = n)
banzhaf(v, method = "appro", n_rep = 2000, n_players = n, replace = TRUE)

v<-c(0,0,0,1,2,1,3)
banzhaf(v, method = "exact")
banzhaf(v, method = "appro", n_rep = 2000, replace = TRUE)

Banzhaf Index (approximated)

Description

Calculate the approximated Banzhaf Index based on sampling

Usage

banzhaf_appro(characteristic_func, n_players, n_rep, replace = TRUE)

Arguments

Value

The Shapley value for each player

Banzhaf Index (exact)

Description

Calculate the approximated Banzhaf Index

Usage

banzhaf_exact(characteristic_func, n_players)

Arguments

Value

The Banzhaf Index for each player

Banzhaf-Owen value

Description

Calculate the Banzhaf-Owen value

Usage

banzhaf_owen(
  characteristic_func,
  union,
  method = "exact",
  n_rep = 10000,
  n_players = 0,
  replace = TRUE
)

Arguments

Value

The Banzhaf-Owen value for each player

Examples

characteristic_func <- c(0,0,0,0,30,30,40,40,50,50,60,70,80,90,100)
union <- list(c(1,3),c(2),c(4))
banzhaf_owen(characteristic_func, union)
banzhaf_owen(characteristic_func, union, method = "appro", n_rep = 4000)

Banzhaf-Owen Value

Description

Calculate the approximated Banzhaf-Owen value

Usage

banzhaf_owen_appro(characteristic_func, union, n_players, n_rep, replace)

Arguments

Value

The Banzhaf-Owen Index for each player

Banzhaf-Owen Value

Description

Calculate the approximated Banzhaf-Owen value

Usage

banzhaf_owen_exact(characteristic_func, union, n_players)

Arguments

Value

The Banzhaf Index for each player

coalitions

Description

Create all the possible coalitions given the number of players

Usage

coalitions(n_players)

Arguments

Value

A list containing a data.frame of the binary representation of the coalitions and a vector of the classical representation (as sets) of the coalitions

Egalitarian value

Description

Calculate the egalitarian value

Usage

egalitarian(characteristic_func, n_players = 0)

Arguments

Value

The egalitarian value for each player

Examples

n <- 10
v <- function(coalition) {
  if (length(coalition) > n/2) {
    return(1)
  } else {
    return(0)
  }
}
egalitarian(v,n)

Equal Surplus Division value

Description

Calculate the equal surplus division value

Usage

equal_surplus_division(characteristic_func, n_players = 0)

Arguments

Value

The equal surplus division value for each player

Examples

n <- 10
v <- function(coalition) {
  if (length(coalition) > n/2) {
    return(1)
  } else {
    return(0)
  }
}
equal_surplus_division(v,n)

Owen value

Description

Calculate the Owen value

Usage

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

Arguments

Value

The Owen value for each player.

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)

Owen value (approximation)

Description

Calculate the approximated Owen value based on sampling

Usage

owen_appro(characteristic_func, union, n_players, n_rep)

Arguments

Value

The Owen value for each player

Owen value (exact)

Description

Calculate the exact Owen

Usage

owen_exact(characteristic_func, union, n_players = NULL)

Arguments

Value

The Owen value for each player

Predecessor

Description

Given a permutation 0 of players and a player i, calculate the set of predecessors of the player i in the order 0

Usage

predecessor(permutation, player, include_player = FALSE)

Arguments

Value

The set of predecessors of the player i in the order 0

Shapley value

Description

Calculate the Shapley value

Usage

shapley(characteristic_func, method = "exact", n_rep = 10000, n_players = 0)

Arguments

Value

The Shapley value for each player.

Examples

n <- 10
v <- function(coalition) {
if (length(coalition) > n/2) {
   return(1)
 } else {
   return(0)
 }
}
shapley(v, method = "appro", n_rep = 4000, n_players = n)

n <- 3
v <- c(1,1,2,1,2,2,2)
shapley(v, method = "exact")
shapley(v, method = "appro", n_rep = 4000)

Shapley value (approximation)

Description

Calculate the approximated Shapley value based on sampling

Usage

shapley_appro(characteristic_func, n_players, n_rep)

Arguments

Value

The Shapley value for each player

Shapley value (exact)

Description

Calculate the exact Shapley value

Usage

shapley_exact(characteristic_func, n_players)

Arguments

Value

The Shapley value for each player