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Title:
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On minimum integer representations of weighted games
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Author:
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Freixas Bosch, Josep; Kurz, Sascha
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III; Universitat Politècnica de Catalunya. GRTJ - Grup de Recerca en Teoria de Jocs |
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Abstract:
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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. |
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Abstract:
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Peer Reviewed |
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Subject(s):
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-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 |
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Rights:
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Document type:
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Article - Submitted version
Article |
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Published by:
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North Holland Mathematical Library
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