Indices of Criticality in Simple Games

Marco Dall’Aglio, Vito Fragnelli () and Stefano Moretti ()
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Marco Dall’Aglio: Department of Economics and Finance, LUISS University, Viale Romania 32, 00197 Roma, Italy
Stefano Moretti: Université Paris Dauphine, PSL Research University, CNRS, LAMSADE, 75775 Paris, France

International Game Theory Review (IGTR), 2019, vol. 21, issue 01, 1-21

Abstract: 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.

Keywords: Simple games; power indices; criticality; weighted majority games; monotonicity (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0219198919400036

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