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On the enumeration of bipartite simple games
dc.contributor.author | Freixas Bosch, Josep |
dc.contributor.author | Samaniego Vidal, Daniel |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.contributor.other | Universitat Politècnica de Catalunya. Doctorat en Matemàtica Aplicada |
dc.date.accessioned | 2021-06-09T14:13:10Z |
dc.date.available | 2023-08-01T00:26:30Z |
dc.date.issued | 2021-07-15 |
dc.identifier.citation | Freixas, J.; Samaniego, D. On the enumeration of bipartite simple games. "Discrete applied mathematics", 15 Juliol 2021, vol. 297, p. 129-141. |
dc.identifier.issn | 0166-218X |
dc.identifier.uri | http://hdl.handle.net/2117/346977 |
dc.description | © 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/ |
dc.description.abstract | 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. |
dc.description.sponsorship | This research has been partially supported by funds from the Ministry of Science, Innovation and Universities grant PID2019-104987GB-I00. |
dc.format.extent | 13 p. |
dc.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 4.0 International |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística |
dc.subject.lcsh | Voting -- Mathematical models |
dc.subject.lcsh | Game theory |
dc.subject.other | Dedekind numbers and simple games |
dc.subject.other | Inequivalent monotonic Boolean functions |
dc.subject.other | Classification of bipartite simple games and bipartite Boolean functions |
dc.subject.other | Enumeration of bipartite simple games and bipartite Boolean functions |
dc.subject.other | Enumeration of the bicameral meet and bicameral join voting systems |
dc.title | On the enumeration of bipartite simple games |
dc.type | Article |
dc.subject.lemac | Vot -- Models matemàtics |
dc.subject.lemac | Jocs, Teoria de |
dc.contributor.group | Universitat Politècnica de Catalunya. GRTJ - Grup de Recerca en Teoria de Jocs |
dc.identifier.doi | 10.1016/j.dam.2021.03.011 |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::40 Sequences, series, summability::40B05 Multiple sequences and series |
dc.subject.ams | Classificació AMS::65 Numerical analysis::65Q05 Difference and functional equations, recurrence relations |
dc.subject.ams | Classificació AMS::68 Computer science::68R Discrete mathematics in relation to computer science |
dc.subject.ams | Classificació AMS::91 Game theory, economics, social and behavioral sciences::91A Game theory |
dc.subject.ams | Classificació AMS::91 Game theory, economics, social and behavioral sciences::91B Mathematical economics |
dc.relation.publisherversion | https://www.sciencedirect.com/science/article/abs/pii/S0166218X21001232 |
dc.rights.access | Open Access |
local.identifier.drac | 31768911 |
dc.description.version | Postprint (author's final draft) |
dc.relation.projectid | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-104987GB-I00/ES/JUEGOS DE VOTACION Y COOPERACION CON APLICACIONES A LAS REDES SOCIALES Y A LAS CIENCIAS POLITICAS/ |
local.citation.author | Freixas, J.; Samaniego, D. |
local.citation.publicationName | Discrete applied mathematics |
local.citation.volume | 297 |
local.citation.startingPage | 129 |
local.citation.endingPage | 141 |
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