On minimum integer representations of weighted games
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 t...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2014 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/24931 |
| Acceso en línea: | https://hdl.handle.net/2117/24931 https://dx.doi.org/10.1016/j.mathsocsci.2013.10.005 |
| Access Level: | acceso abierto |
| Palabra clave: | 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 Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Teoria de jocs |
| Sumario: | 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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