banzhaf_owen_appro

Calculate the approximated Banzhaf-Owen value using the
algorithm proposed by Saavedra-Nieves &amp; Fiestras-Janeiro (2021).

The main objective of cooperative Transferable-Utility games (TU-games)
is to allocate a good among the agents involved. The package implements major
solution concepts including the Shapley value, Banzhaf value, and egalitarian
rules, alongside their extensions for structured games:
the Owen value and Banzhaf-Owen value for games with a priori unions, and the
Myerson value for communication games on networks. To address the inherent exponential
computational complexity of exact evaluation, the package offers both exact
algorithms and linear approximation methods based on sampling, enabling the
analysis of large-scale games. Additionally, it supports core set-based
solutions, allowing computation of the vertices and the centroid of the core.

Maria D. Guillen

TUvalues

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

Juan Carlos Gonçalves

banzhaf_owen_appro function

<dl><dt>characteristic_func</dt>
<dd>The valued function defined on the subsets of the number
of players</dd>
<dt>union</dt>
<dd>List of vectors indicating the a priori unions between the
players</dd>
<dt>n_players</dt>
<dd>The number of players</dd>
<dt>n_rep</dt>
<dd>Only used if <code>method</code> is <code>appro</code>. The number of
iterations to perform in the approximated calculation.</dd>
<dt>replace</dt>
<dd>Should sampling be with replacement?</dd>
<dt>echo</dt>
<dd>Show progress of the calculation.</dd></dl>

Arguments

Banzhaf-Owen Value — banzhaf_owen_appro

<dl>

<dt>characteristic_func</dt>
<dd>The valued function defined on the subsets of the number
of players</dd>


<dt>union</dt>
<dd>List of vectors indicating the a priori unions between the
players</dd>


<dt>n_players</dt>
<dd>The number of players</dd>


<dt>n_rep</dt>
<dd>Only used if <code>method</code> is <code>appro</code>. The number of
iterations to perform in the approximated calculation.</dd>


<dt>replace</dt>
<dd>Should sampling be with replacement?</dd>


<dt>echo</dt>
<dd>Show progress of the calculation.</dd>

</dl>

banzhaf_owen_appro: Banzhaf-Owen Value

Description

Usage

Value

Arguments

References