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Title:
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On the characterization of weighted simple games
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Author:
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Freixas Bosch, Josep; Freixas Boleda, Marc; Kurz, Sascha
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. GRTJ - Grup de Recerca en Teoria de Jocs; Universitat Politècnica de Catalunya. GIE - Grup d'Informàtica a l'Enginyeria |
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Abstract:
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The final publication is available at link.springer.com via http://dx.doi.org/10.1007/s11238-017-9606-z |
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Abstract:
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This paper has a twofold scope. The first one is to clarify and put in evidence the isomorphic character of two theories developed in quite different fields: on one side, threshold logic, on the other side, simple games. One of the main purposes in both theories is to determine when a simple game is representable as a weighted game, which allows a very compact and easily comprehensible representation. Deep results were found in threshold logic in the sixties and seventies for this problem. However, game theory has taken the lead and some new results have been obtained for the problem in the past two decades. The second and main goal of this paper is to provide some new results on this problem and propose several open questions and conjectures for future research. The results we obtain depend on two significant parameters of the game: the number of types of equivalent players and the number of types of shift-minimal winning coalitions. |
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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
-Simple games
-Weighted games
-Characterization of weighted games
-Trade robustness
-Invariant-trade robustness
-Jocs, Teoria de
-Classificació AMS::06 Order, lattices, ordered algebraic structures::06E Boolean algebras (Boolean rings)
-Classificació AMS::91 Game theory, economics, social and behavioral sciences::91A Game theory
-Classificació AMS::92 Biology and other natural sciences::92B Mathematical biology in general
-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
Book Part |
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