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Dynamic Programming for Computing Power Indices for Weighted Voting Games with Precoalitions

  • We study the efficient computation of power indices for weighted voting games with precoalitions amongst subsets of players (reflecting, e.g., ideological proximity) using the paradigm of dynamic programming. Starting from the state-of-the-art algorithms for computing the Banzhaf and Shapley–Shubik indices for weighted voting games, we present a framework for fast algorithms for the three most common power indices with precoalitions, i.e., the Owen index, the Banzhaf–Owen index and the symmetric coalitional Banzhaf index, and point out why our new algorithms are applicable for large numbers of players. We discuss implementations of our algorithms for the three power indices with precoalitions in C++ and review computing times, as well as storage requirements.

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Metadaten
Author:Jochen StaudacherORCiDGND, Felix Wagner, Jan Filipp
DOI:https://doi.org/10.3390/g13010006
Identifier:2073-4336 OPAC HS OPAC extern
Parent Title (English):Games
Publisher:MDPI
Place of publication:Basel
Document Type:Article
Language:English
Date of Publication (online):2021/12/26
Year of first Publication:2022
Tag:Dynamic Programming; Owen value; Precoalitions; Weighted Voting Games
GND Keyword:Spieltheorie; Dynamische Optimierung
Volume:2022
Issue:13 / 1
Number of pages:17 Seiten
First Page:1
Last Page:17
Institutes:Fakultät Informatik
IFI - Institut für Internationalisierung
Dewey Decimal Classification:0 Informatik, Informationswissenschaft, allgemeine Werke
3 Sozialwissenschaften
Open Access:open_access
Research focus:FSP4: Soziale Innovationen
Publication Lists:Staudacher, Jochen
Publication reviewed:begutachtet
Licence (German):Creative Commons - CC BY - Namensnennung 4.0 International
Release Date:2022/01/11
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