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dc.contributor.authorFreixas Bosch, Josep
dc.contributor.authorMolinero Albareda, Xavier
dc.contributor.authorOlsen, Martin
dc.contributor.authorSerna Iglesias, María José
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Ciències de la Computació
dc.identifier.citationFreixas, J. [et al.]. On the complexity of problems on simple games. "RAIRO. Operations research", Octubre 2011, p. 295-314.
dc.descriptionThe original publication is available at
dc.description.abstractSimple games cover voting systems in which a single alter- native, such as a bill or an amendment, is pitted against the status quo. A simple game or a yes-no voting system is a set of rules that specifies exactly which collections of “yea” votes yield passage of the issue at hand. Each of these collections of “yea” voters forms a winning coalition. We are interested in performing a complexity analysis on problems defined on such families of games. This analysis as usual depends on the game representation used as input. We consider four natural explicit representations: winning, losing, minimal winning, and maximal losing. We first analyze the complexity of testing whether a game is simple and testing whether a game is weighted. We show that, for the four types of representations, both problems can be solved in polynomial time. Finally, we provide results on the complexity of testing whether a simple game or a weighted game is of a special type. We analyze strongness, properness, weightedness, homogeneousness, decisiveness and majorityness, which are desirable properties to be fulfilled for a simple game. Finally, we consider the possibility of representing a game in a more succinct and natural way and show that the corresponding recognition problem is hard.
dc.format.extent20 p.
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Teoria de jocs
dc.subject.lcshVoting--Mathematical models
dc.subject.lcshGame theory
dc.subject.otherMajority games
dc.titleOn the complexity of problems on 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.contributor.groupUniversitat Politècnica de Catalunya. ALBCOM - Algorismia, Bioinformàtica, Complexitat i Mètodes Formals
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::91 Game theory, economics, social and behavioral sciences::91A Game theory
dc.rights.accessOpen Access
dc.description.versionPostprint (published version)
local.citation.authorFreixas, J.; Molinero, X.; Olsen, M.; Serna, M.
local.citation.publicationNameRAIRO. Operations research

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