Academic Journal
On the enumeration of bipartite simple games
| Τίτλος: | On the enumeration of bipartite simple games |
|---|---|
| Συγγραφείς: | Josep Freixas, Dani Samaniego |
| Συνεισφορές: | Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. Doctorat en Matemàtica Aplicada, Universitat Politècnica de Catalunya. GRTJ - Grup de Recerca en Teoria de Jocs |
| Πηγή: | UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) |
| Στοιχεία εκδότη: | Elsevier BV, 2021. |
| Έτος έκδοσης: | 2021 |
| Θεματικοί όροι: | Classificació AMS::91 Game theory, economics, social and behavioral sciences::91B Mathematical economics, recurrence relations, Classificació AMS::65 Numerical analysis::65Q05 Difference and functional equations, recurrence relations, social and behavioral sciences::91B Mathematical economics, 0211 other engineering and technologies, Classification of bipartite simple games and bipartite Boolean functions, 02 engineering and technology, social and behavioral sciences::91A Game theory, Inequivalent monotonic Boolean functions, 0502 economics and business, 91 Game theory, economics, social and behavioral sciences::91B Mathematical economics [Classificació AMS], series, Enumeration of bipartite simple games and bipartite Boolean functions, Vot -- Models matemàtics, Voting -- Mathematical models, Jocs, Teoria de, 68 Computer science::68R Discrete mathematics in relation to computer science [Classificació AMS], Classificació AMS::91 Game theory, economics, social and behavioral sciences::91A Game theory, Game theory, 65 Numerical analysis::65Q05 Difference and functional equations, recurrence relations [Classificació AMS], Àrees temàtiques de la UPC::Matemàtiques i estadística, Teoria de, Dedekind numbers and simple games, 05 social sciences, Classificació AMS::91 Game theory, Matemàtiques i estadística [Àrees temàtiques de la UPC], economics, 91 Game theory, economics, social and behavioral sciences::91A Game theory [Classificació AMS], Jocs, Classificació AMS::65 Numerical analysis::65Q05 Difference and functional equations, Classificació AMS::68 Computer science::68R Discrete mathematics in relation to computer science, 40 Sequences, series, summability::40B05 Multiple sequences and series [Classificació AMS], Classificació AMS::40 Sequences, Enumeration of the bicameral meet and bicameral join voting systems, summability::40B05 Multiple sequences and series, Classificació AMS::40 Sequences, series, summability::40B05 Multiple sequences and series |
| Περιγραφή: | © 2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ This 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. This research has been partially supported by funds from the Ministry of Science, Innovation and Universities grant PID2019-104987GB-I00. |
| Τύπος εγγράφου: | Article |
| Περιγραφή αρχείου: | application/pdf |
| Γλώσσα: | English |
| ISSN: | 0166-218X |
| DOI: | 10.1016/j.dam.2021.03.011 |
| DOI: | 10.13039/501100011033 |
| Rights: | Elsevier Non-Commercial CC BY NC ND |
| Αριθμός Καταχώρησης: | edsair.doi.dedup.....db7ead8a45e959c646e63c9a1f01a3f2 |
| Βάση Δεδομένων: | OpenAIRE |
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This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ This 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. This research has been partially supported by funds from the Ministry of Science, Innovation and Universities grant PID2019-104987GB-I00. – Name: TypeDocument Label: Document Type Group: TypDoc Data: Article – Name: Format Label: File Description Group: SrcInfo Data: application/pdf – Name: Language Label: Language Group: Lang Data: English – Name: ISSN Label: ISSN Group: ISSN Data: 0166-218X – Name: DOI Label: DOI Group: ID Data: 10.1016/j.dam.2021.03.011 – Name: DOI Label: DOI Group: ID Data: 10.13039/501100011033 – Name: Copyright Label: Rights Group: Cpyrght Data: Elsevier Non-Commercial<br />CC BY NC ND – Name: AN Label: Accession Number Group: ID Data: edsair.doi.dedup.....db7ead8a45e959c646e63c9a1f01a3f2 |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.dam.2021.03.011 Languages: – Text: English PhysicalDescription: Pagination: PageCount: 13 StartPage: 129 Subjects: – SubjectFull: Classificació AMS::91 Game theory, economics, social and behavioral sciences::91B Mathematical economics Type: general – SubjectFull: recurrence relations Type: general – SubjectFull: Classificació AMS::65 Numerical analysis::65Q05 Difference and functional equations, recurrence relations Type: general – SubjectFull: social and behavioral sciences::91B Mathematical economics Type: general – SubjectFull: 0211 other engineering and technologies Type: general – SubjectFull: Classification of bipartite simple games and bipartite Boolean functions Type: general – SubjectFull: 02 engineering and technology Type: general – SubjectFull: social and behavioral sciences::91A Game theory Type: general – SubjectFull: Inequivalent monotonic Boolean functions Type: general – SubjectFull: 0502 economics and business Type: general – SubjectFull: 91 Game theory, economics, social and behavioral sciences::91B Mathematical economics [Classificació AMS] Type: general – SubjectFull: series Type: general – SubjectFull: Enumeration of bipartite simple games and bipartite Boolean functions Type: general – SubjectFull: Vot -- Models matemàtics Type: general – SubjectFull: Voting -- Mathematical models Type: general – SubjectFull: Jocs, Teoria de Type: general – SubjectFull: 68 Computer science::68R Discrete mathematics in relation to computer science [Classificació AMS] Type: general – SubjectFull: Classificació AMS::91 Game theory, economics, social and behavioral sciences::91A Game theory Type: general – SubjectFull: Game theory Type: general – SubjectFull: 65 Numerical analysis::65Q05 Difference and functional equations, recurrence relations [Classificació AMS] Type: general – SubjectFull: Àrees temàtiques de la UPC::Matemàtiques i estadística Type: general – SubjectFull: Teoria de Type: general – SubjectFull: Dedekind numbers and simple games Type: general – SubjectFull: 05 social sciences Type: general – SubjectFull: Classificació AMS::91 Game theory Type: general – SubjectFull: Matemàtiques i estadística [Àrees temàtiques de la UPC] Type: general – SubjectFull: economics Type: general – SubjectFull: 91 Game theory, economics, social and behavioral sciences::91A Game theory [Classificació AMS] Type: general – SubjectFull: Jocs Type: general – SubjectFull: Classificació AMS::65 Numerical analysis::65Q05 Difference and functional equations Type: general – SubjectFull: Classificació AMS::68 Computer science::68R Discrete mathematics in relation to computer science Type: general – SubjectFull: 40 Sequences, series, summability::40B05 Multiple sequences and series [Classificació AMS] Type: general – SubjectFull: Classificació AMS::40 Sequences Type: general – SubjectFull: Enumeration of the bicameral meet and bicameral join voting systems Type: general – SubjectFull: summability::40B05 Multiple sequences and series Type: general – SubjectFull: Classificació AMS::40 Sequences, series, summability::40B05 Multiple sequences and series Type: general Titles: – TitleFull: On the enumeration of bipartite simple games Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Josep Freixas – PersonEntity: Name: NameFull: Dani Samaniego – PersonEntity: Name: NameFull: Universitat Politècnica de Catalunya. Departament de Matemàtiques – PersonEntity: Name: NameFull: Universitat Politècnica de Catalunya. Doctorat en Matemàtica Aplicada – PersonEntity: Name: NameFull: Universitat Politècnica de Catalunya. GRTJ - Grup de Recerca en Teoria de Jocs IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 07 Type: published Y: 2021 Identifiers: – Type: issn-print Value: 0166218X – Type: issn-locals Value: edsair – Type: issn-locals Value: edsairFT Numbering: – Type: volume Value: 297 Titles: – TitleFull: Discrete Applied Mathematics Type: main |
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