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Preorders in simple games
dc.contributor.author | Freixas Bosch, Josep |
dc.contributor.author | Pons Vallès, Montserrat |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2018-01-31T10:31:34Z |
dc.date.issued | 2017 |
dc.identifier.citation | Freixas, J., Pons, M. Preorders in simple games. A: "Transactions on computational collective intelligence XXVII". Berlín: Springer, 2017 (Lecture notes in computer science; 10480). p. 63-73. |
dc.identifier.isbn | 978-3-319-70646-7 |
dc.identifier.uri | http://hdl.handle.net/2117/113429 |
dc.description | The final authenticated version is available online at: https://doi.org/10.1007/978-3-319-70647-4_5. |
dc.description.abstract | Any power index defines a total preorder in a simple game and, thus, induces a hierarchy among its players. The desirability relation, which is also a preorder, induces the same hierarchy as the Banzhaf and the Shapley indices on linear games, i.e., games in which the desirability relation is total. The desirability relation is a sub–preorder of another preorder, the weak desirability relation, and the class of weakly linear games, i.e., games for which the weak desirability relation is total, is larger than the class of linear games. The weak desirability relation induces the same hierarchy as the Banzhaf and the Shapley indices on weakly linear games. In this paper, we define a chain of preorders between the desirability and the weak desirability preorders. From them we obtain new classes of totally preordered games between linear and weakly linear games. |
dc.format.extent | 11 p. |
dc.language.iso | eng |
dc.publisher | Springer |
dc.relation.ispartof | Lecture notes in computer science (10480) |
dc.relation.ispartof | Transactions on computational collective intelligence (10480) |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Teoria de jocs |
dc.subject.lcsh | Game theory |
dc.subject.lcsh | Hierarchies |
dc.subject.other | Simple game |
dc.subject.other | Power index |
dc.subject.other | Preorder |
dc.subject.other | Desirability |
dc.subject.other | Weak desirability |
dc.subject.other | Linear game |
dc.subject.other | Weakly linear game |
dc.title | Preorders in simple games |
dc.type | Part of book or chapter of book |
dc.subject.lemac | Jocs, Teoria de |
dc.contributor.group | Universitat Politècnica de Catalunya. GRTJ - Grup de Recerca en Teoria de Jocs |
dc.identifier.doi | 10.1007/978-3-319-70647-4_5 |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::91 Game theory, economics, social and behavioral sciences::91A Game theory |
dc.relation.publisherversion | https://link.springer.com/chapter/10.1007/978-3-319-70647-4_5 |
dc.rights.access | Open Access |
local.identifier.drac | 21676697 |
dc.description.version | Postprint (author's final draft) |
dc.relation.projectid | info:eu-repo/grantAgreement/MINECO//MTM2015-66818-P/ES/ASPECTOS MATEMATICOS, COMPUTACIONALES Y SOCIALES EN CONTEXTOS DE VOTACION Y DE COOPERACION./ |
local.citation.author | Freixas, J.; Pons, M. |
local.citation.pubplace | Berlín |
local.citation.publicationName | Transactions on computational collective intelligence XXVII |
local.citation.startingPage | 63 |
local.citation.endingPage | 73 |
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