On ordinal equivalence of the Shapley and Banzhaf values for cooperative games

DOI10.1007/s00182-009-0179-0zbMath1211.91033OpenAlexW1970022167MaRDI QIDQ532752

Josep Freixas

Publication date: 5 May 2011

Published in: International Journal of Game Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00182-009-0179-0

zbMATH Keywords

cooperative gamesemivaluecoherent gamesemicoherent gameweakly complete game

Mathematics Subject Classification ID

Cooperative games (91A12) Voting theory (91B12) Other game-theoretic models (91A40)

Related Items (21)

The fairness of solidarity bills under the solidarity value of Nowak and Radzik ⋮ A three-dimensional voting system in Hong Kong ⋮ Success and decisiveness on proper symmetric games ⋮ Ordinal equivalence of values, Pigou-Dalton transfers and inequality in TU-games ⋮ The conditional Shapley-Shubik measure for ternary voting games ⋮ Ranking objects from a preference relation over their subsets ⋮ On the ordinal equivalence of the Johnston, Banzhaf and Shapley power indices ⋮ The influence relation for ternary voting games ⋮ On the enumeration of some inequivalent monotone Boolean functions ⋮ Linear symmetric rankings for TU-games ⋮ Probabilistic power indices for voting rules with abstention ⋮ A new family of regular semivalues and applications ⋮ Hierarchy of players in swap robust voting games ⋮ Egalitarian property for power indices ⋮ Enumeration of weighted games with minimum and an analysis of voting power for bipartite complete games with minimum ⋮ Nash-stable coalition partition and potential functions in games with coalition structure ⋮ On the ordinal equivalence of the Jonhston, Banzhaf and Shapley-Shubik power indices for voting games with abstention ⋮ A non-parametric approach to testing the axioms of the Shapley value with limited data ⋮ POWER SHARING IN POLITICS ⋮ SOME OPEN PROBLEMS IN SIMPLE GAMES ⋮ Ranking sets of interacting objects via semivalues

Cites Work

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• On coalitional semivalues
• A class of simple games
• Achievable hierarchies in voting games
• Complete simple games
• Semivalues as power indices.
• Ordinal equivalence of power notions in voting games
• Hierarchies achievable in simple games
• Circumstantial power: Optimal persuadable voters
• On ordinal equivalence of power measures given by regular semivalues
• Value Theory Without Efficiency
• Multilinear extensions and the banzhaf value
• Characterization of the Banzhaf–Coleman Index

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