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Indices of criticality in simple games

Dall'Aglio, Marco; Fragnelli, Vito; Moretti, Stefano (2019), Indices of criticality in simple games, International Game Theory Review, 21, 1, p. 1-21. 10.1142/S0219198919400036

Type
Article accepté pour publication ou publié
Date
2019
Journal name
International Game Theory Review
Volume
21
Number
1
Publisher
World Scientific
Pages
1-21
Publication identifier
Metadata
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Author(s)
Dall'Aglio, Marco
Department of Economics and Finance
Fragnelli, Vito
University of eastern piedmont of Novara
Moretti, Stefano cc
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Abstract (EN)
Power indices in simple games measure the relevance of a player through her ability in being critical, i.e. essential for a coalition to win. We introduce new indices that measure the power of a player in being decisive through the collaboration of other players. We study the behavior of these criticality indices to compare the power of different players within a single voting situation, and that of the same player with varying weight across different voting situations. In both cases we establish monotonicity results in line with those of Turnovec [1998]. Finally, we examine which properties characterizing the indices of Shapley–Shubik and Banzhaf are shared by these new indices.
Subjects / Keywords
Simple games; power indices; criticality; weighted majority games; monotonicity