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dc.contributor.authorFreixas Bosch, Josep
dc.contributor.authorSamaniego Vidal, Daniel
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.contributor.otherUniversitat Politècnica de Catalunya. Doctorat en Matemàtica Aplicada
dc.identifier.citationFreixas, J.; Samaniego, D. On the enumeration of bipartite simple games. "Discrete applied mathematics", 15 Juliol 2021, vol. 297, p. 129-141.
dc.description© 2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 license
dc.description.abstractThis paper provides a classification of all monotonic bipartite simple games. The problem we deal with is very versatile since simple games are inequivalent monotonic Boolean functions, functions that are used in many fields such as game theory, neural networks, artificial intelligence, reliability or multiple-criteria decision-making. The obtained classification can be implemented in an algorithm able to enumerate bipartite simple games. These numbers provide some light on enumerations of several subclasses of bipartite simple games, for which we find formulas. Complete simple games, a subclass of all simple games for which the desirability relation is a complete preordering, were already classified by means of two parameters: a vector and a matrix fulfilling some conditions. Complete simple games are inequivalent monotonic regular Boolean functions. In this paper, we deduce a procedure for bipartite non-complete games, which allows enumerating the number of bipartite simple games. Several formulas are obtained, in particular polynomial expressions for the number of bicameral meet games and the number of bicameral join games, two types of voting systems widely used in practice.
dc.description.sponsorshipThis research has been partially supported by funds from the Ministry of Science, Innovation and Universities grant PID2019-104987GB-I00.
dc.format.extent13 p.
dc.rightsAttribution-NonCommercial-NoDerivs 4.0 International
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject.lcshVoting -- Mathematical models
dc.subject.lcshGame theory
dc.subject.otherDedekind numbers and simple games
dc.subject.otherInequivalent monotonic Boolean functions
dc.subject.otherClassification of bipartite simple games and bipartite Boolean functions
dc.subject.otherEnumeration of bipartite simple games and bipartite Boolean functions
dc.subject.otherEnumeration of the bicameral meet and bicameral join voting systems
dc.titleOn the enumeration of bipartite simple games
dc.subject.lemacVot -- Models matemàtics
dc.subject.lemacJocs, Teoria de
dc.contributor.groupUniversitat Politècnica de Catalunya. GRTJ - Grup de Recerca en Teoria de Jocs
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::40 Sequences, series, summability::40B05 Multiple sequences and series
dc.subject.amsClassificació AMS::65 Numerical analysis::65Q05 Difference and functional equations, recurrence relations
dc.subject.amsClassificació AMS::68 Computer science::68R Discrete mathematics in relation to computer science
dc.subject.amsClassificació AMS::91 Game theory, economics, social and behavioral sciences::91A Game theory
dc.subject.amsClassificació AMS::91 Game theory, economics, social and behavioral sciences::91B Mathematical economics
dc.rights.accessRestricted access - publisher's policy
dc.description.versionPostprint (author's final draft)
local.citation.authorFreixas, J.; Samaniego, D.
local.citation.publicationNameDiscrete applied mathematics

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