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Title:
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On a-roughly 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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Gvozdeva, Hemaspaandra, and Slinko (2011) have introduced three hierarchies for simple games in order to measure the distance of a given simple game to the class of (roughly) weighted voting games. Their third class C-alpha consists of all simple games permitting a weighted representation such that each winning coalition has a weight of at least and each losing coalition a weight of at most alpha. For a given game the minimal possible value of alpha is called its critical threshold value. We continue the work on the critical threshold value, initiated by Gvozdeva et al., and contribute some new results on the possible values for a given number of voters as well as some general bounds for restricted subclasses of games. A strong relation between this concept and the cost of stability, i.e. the minimum amount of external payment to ensure stability in a coalitional game, is uncovered. |
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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
-Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Teoria de jocs
-Voting--Mathematical models
-Game theory
-Simple game
-Weighted game
-Complete simple game
-Roughly weighted game
-Voting theory
-Hierarchy
-Vot -- Models matemàtics
-Jocs, Teoria de
-Classificació AMS::91 Game theory, economics, social and behavioral sciences::91B Mathematical economics
-Classificació AMS::94 Information And Communication, Circuits::94C Circuits, networks |
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Rights:
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Document type:
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Article - Submitted version
Article |
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