1. Enumeration of weighted games with minimum and an analysis of voting power for bipartite complete games with minimum
- Author
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Sascha Kurz, Josep Freixas, Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III, and Universitat Politècnica de Catalunya. GRTJ - Grup de Recerca en Teoria de Jocs
- Subjects
Ordinal equivalence ,System ,Computer Science::Computer Science and Game Theory ,media_common.quotation_subject ,Semivalues ,Simple game ,General Decision Sciences ,Management Science and Operations Research ,Type (model theory) ,Combinatorics ,Enumerations ,Europena Union ,Simple (abstract algebra) ,Weighted and complete games ,Voting ,FOS: Mathematics ,91 Game theory, economics, social and behavioral sciences::91B Mathematical economics [Classificació AMS] ,Enumeration ,Mathematics - Combinatorics ,Rank (graph theory) ,Vot -- Models matemàtics ,Jocs, Teoria de ,Special case ,Shapley-Shubik power index ,Matemàtiques i estadística::Investigació operativa::Teoria de jocs [Àrees temàtiques de la UPC] ,Game theory ,Mathematics ,media_common ,Discrete mathematics ,Shapley–Shubik power index ,Banzhaf power indices ,Banzhaf power index ,ComputingMilieux_PERSONALCOMPUTING ,Indexes ,91 Game theory, economics, social and behavioral sciences::91A Game theory [Classificació AMS] ,Bipartite graph ,Voting--Mathematical models ,Council ,Combinatorics (math.CO) ,91A12, 91A40, 91A80, 91B12 ,Dimension ,Focus (optics) - Abstract
This paper is a twofold contribution. First, it contributes to the problem of enumerating some classes of simple games and in particular provides the number of weighted games with minimum and the number of weighted games for the dual class as well. Second, we focus on the special case of bipartite complete games with minimum, and we compare and rank these games according to the behavior of some efficient power indices of players of type 1 (or of type 2). The main result of this second part establishes all allowable rankings of these games when the Shapley-Shubik power index is used on players of type 1., 26 pages, 2 figures, to appear in Annals of Operations Research
- Published
- 2013
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