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On minimum integer representations of weighted games
Freixas Bosch, Josep; Kurz, Sascha
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III; Universitat Politècnica de Catalunya. GRTJ - Grup de Recerca en Teoria de Jocs
We study minimum integer representations of weighted games, i.e. representations where the weights are integers and every other integer representation is at least as large in each component. Those minimum integer representations, if they exist at all, are linked with some solution concepts in game theory. Closing existing gaps in the literature, we prove that each weighted game with two types of voters admits a (unique) minimum integer representation, and give new examples for more than two types of voters without a minimum integer representation. We characterize the possible weights in minimum integer representations and give examples for t >= 4 types of voters without a minimum integer representation preserving types, i.e. where we additionally require that the weights are equal within equivalence classes of voters. (C) 2013 Elsevier B.V. All rights reserved.
Peer Reviewed
Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Teoria de jocs
Game theory
Voting--Mathematical models
Weighted games
Minimum integer representations
Representations with minimum sum
Jocs, Teoria de
Vot -- Models matemàtics
Classificació AMS::90 Operations research, mathematical programming::90C Mathematical programming
Classificació AMS::91 Game theory, economics, social and behavioral sciences::91A Game theory
Classificació AMS::91 Game theory, economics, social and behavioral sciences::91B Mathematical economics
info:eu-repo/semantics/submittedVersion
Artículo
North Holland Mathematical Library
         

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