Computing Banzhaf-Coleman and Shapley-Shubik power indices with incompatible players

DOI10.1016/j.amc.2014.12.011zbMath1338.91014OpenAlexW1982653122MaRDI QIDQ298742

Balbina V. Casas Méndez, José M. Alonso-Meijide, María Gloria Fiestras-Janeiro

Publication date: 21 June 2016

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2014.12.011

zbMATH Keywords

generating functionsShapley-Shubik power indexweighted majority gamesBanzhaf-Coleman power indexincompatible players

Mathematics Subject Classification ID

Applications of graph theory (05C90) Cooperative games (91A12) Games involving graphs (91A43) Voting theory (91B12)

Related Items (6)

An approach via generating functions to compute power indices of multiple weighted voting games with incompatible players ⋮ Generating Functions of Weighted Voting Games, MacMahon’s Partition Analysis, and Clifford Algebras ⋮ Voting power on a graph connected political space with an application to decision-making in the council of the European Union ⋮ Set-weighted games and their application to the cover problem ⋮ Monte Carlo methods for the Shapley-Shubik power index ⋮ Measuring power in coalitional games with friends, enemies and allies

Uses Software

• Algorithm 457

Cites Work

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• Generating functions for computing the Myerson value
• Evaluating correct classification probability for weighted voting classifiers with plurality voting
• Computation of several power indices by generating functions
• Evaluation of Banzhaf index with restrictions on coalitions formation
• Cooperation when some players are incompatible
• Values of Graph-Restricted Games
• Graphs and Cooperation in Games
• Threshold optimization for weighted voting classifiers
• The Enumeration of Maximal Cliques of Large Graphs
• Algorithm 457: finding all cliques of an undirected graph
• Generating functions for computing power indices efficiently

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