Name: A characterization of weighted simple games based on pseudoweightings
Creator: Freixas Bosch, Josep
Keywords: Classificació AMS::91 Game theory, economics, social and behavioral sciences::91B Mathematical economics, Optimization, Threshold logic, Optimització matemàtica, social and behavioral sciences::91B Mathematical economics, 0211 other engineering and technologies, Classificació AMS::94 Information And Communication, Simple games, 02 engineering and technology, 01 natural sciences

descriptionPublicationkeyboard_double_arrow_right Article 14 Sep 2020 English Publisher:Springer Science and Business Media LLCJournal:Optimization Letters, volume 15, pages 1,371-1,383 (issn: 1862-4472, eissn: 1862-4480,

Authors: Freixas Bosch, Josep;

doi: 10.1007/s11590-020-01647-3

handle: 2117/337122

A characterization of weighted simple games based on pseudoweightings

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Abstract

This is a post-peer-review, pre-copyedit version of an article published in Optimization letters. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11590-020-01647-3 The paper provides a new characterization of weighted games within the class of simple games. It is based on a stronger form of the point-set-additive pseudoweighting property of simple games. The characterization obtained is of interest in various research fields such as game theory, coherent structures, logic gates, operations research and Boolean algebra. A (monotonic) simple game corresponds to an inequivalent (monotonic) function in Boolean algebra and a weighted game corresponds to a threshold function. The characterization obtained provides a better understanding of these mathematical structures while opening new prospects for solving numerous open problems in these areas. This research was partially supported by funds from the Spanish Ministry of Economy and Competitiveness (MINECO) and from the European Union (FEDER funds) under grant MTM2015–66818-P(MINECO/FEDER). Peer Reviewed

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Classificació AMS::91 Game theory, economics, social and behavioral sciences::91B Mathematical economics, Optimization, Threshold logic, Optimització matemàtica, social and behavioral sciences::91B Mathematical economics, Classificació AMS::94 Information And Communication, Simple games, Classificació AMS::90 Operations research, mathematical programming::90B Operations research and management science, Threshold functions, Algebra, Boolean, social and behavioral sciences::91A Game theory, :90 Operations research, mathematical programming::90B Operations research and management science [Classificació AMS], Classificació AMS::06 Order, ordered algebraic structures::06E Boolean algebras (Boolean rings), :91 Game theory, economics, social and behavioral sciences::91B Mathematical economics [Classificació AMS], Boolean functions, Jocs, Teoria de, Classificació AMS::91 Game theory, economics, social and behavioral sciences::91A Game theory, Game theory, :Matemàtiques i estadística::Investigació operativa::Teoria de jocs [Àrees temàtiques de la UPC], Classificació AMS::90 Operations research, Teoria de, Circuits::94C Circuits, Mathematical optimization, Classificació AMS::06 Order, lattices, ordered algebraic structures::06E Boolean algebras (Boolean rings), Classificació AMS::91 Game theory, Classificació AMS::94 Information And Communication, Circuits::94C Circuits, networks, Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Teoria de jocs, Pseudoweightings, economics, :91 Game theory, economics, social and behavioral sciences::91A Game theory [Classificació AMS], Jocs, :06 Order, lattices, ordered algebraic structures::06E Boolean algebras (Boolean rings) [Classificació AMS], :94 Information And Communication, Circuits::94C Circuits, networks [Classificació AMS], Algebra, mathematical programming::90B Operations research and management science, lattices, networks, Weighted games, Boolean, Àlgebra booleana

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