GRTJ - Grup de Recerca en Teoria de Jocs
http://hdl.handle.net/2117/3429
2017-03-24T18:28:03ZAbility to separate situations with a priori coalition structures by means of symmetric solutions
http://hdl.handle.net/2117/102517
Ability to separate situations with a priori coalition structures by means of symmetric solutions
Giménez Pradales, José Miguel
We say that two situations described by cooperative games are inseparable by a family of solutions, when they obtain the same allocation by all solution concept of this family. The situation of separability by a family of linear solutions reduces to separability from the null game. This is the case of the family of solutions based on marginal contributions weighted by coef¿cients only dependent of the coalition size: the semivalues. It is known that for games with four or more players, the spaces of inseparable games from the null game contain games different to zero-game. We will prove that for ¿ve or more players, when a priori coalition blocks are introduced in the situation described by the game, the dimension of the vector spaces of inseparable games from the null game decreases in an important manner.
2017-03-15T13:33:58ZGiménez Pradales, José MiguelWe say that two situations described by cooperative games are inseparable by a family of solutions, when they obtain the same allocation by all solution concept of this family. The situation of separability by a family of linear solutions reduces to separability from the null game. This is the case of the family of solutions based on marginal contributions weighted by coef¿cients only dependent of the coalition size: the semivalues. It is known that for games with four or more players, the spaces of inseparable games from the null game contain games different to zero-game. We will prove that for ¿ve or more players, when a priori coalition blocks are introduced in the situation described by the game, the dimension of the vector spaces of inseparable games from the null game decreases in an important manner.Effect of a science communication event on students’ attitudes towards science and technology
http://hdl.handle.net/2117/102416
Effect of a science communication event on students’ attitudes towards science and technology
Torras Melenchón, Núria; Grau Vilalta, Maria Dolors; Font Soldevila, Josep; Freixas Bosch, Josep
2017-03-14T08:15:19ZTorras Melenchón, NúriaGrau Vilalta, Maria DolorsFont Soldevila, JosepFreixas Bosch, JosepA new procedure to calculate the Owen value
http://hdl.handle.net/2117/102250
A new procedure to calculate the Owen value
Puente del Campo, María Albina; Giménez Pradales, José Miguel
In this paper we focus on games with a coalition structure. Particularly, we deal with the Owen value, the coalitional value of the Shapley value, and we provide a computational procedure to calculate this coalitional value in terms of the multilinear extension of the original game.
2017-03-09T19:07:48ZPuente del Campo, María AlbinaGiménez Pradales, José MiguelIn this paper we focus on games with a coalition structure. Particularly, we deal with the Owen value, the coalitional value of the Shapley value, and we provide a computational procedure to calculate this coalitional value in terms of the multilinear extension of the original game.Measuring satisfaction in societies with opinion leaders and mediators
http://hdl.handle.net/2117/101810
Measuring satisfaction in societies with opinion leaders and mediators
Molinero Albareda, Xavier; Riquelme Csori, F.; Serna Iglesias, María José
An opinion leader-follower model (OLF) is a two-action collective decision-making model for societies, in which three kinds of actors are considered:
2017-03-01T16:19:14ZMolinero Albareda, XavierRiquelme Csori, F.Serna Iglesias, María JoséAn opinion leader-follower model (OLF) is a two-action collective decision-making model for societies, in which three kinds of actors are considered:Decisiveness indices are semiindices: addendum
http://hdl.handle.net/2117/98770
Decisiveness indices are semiindices: addendum
Freixas Bosch, Josep; Pons Vallès, Montserrat
In the paper Decisiveness indices are semiindices (Freixas and Pons, 2016) it was shown that any decisiveness index obtained from an anonymous probability distribution is a semiindex, and that the converse is not true. In this note we characterize the semiindices which are indices of decisiveness.
2016-12-22T15:36:17ZFreixas Bosch, JosepPons Vallès, MontserratIn the paper Decisiveness indices are semiindices (Freixas and Pons, 2016) it was shown that any decisiveness index obtained from an anonymous probability distribution is a semiindex, and that the converse is not true. In this note we characterize the semiindices which are indices of decisiveness.On the construction of high dimensional simple games
http://hdl.handle.net/2117/97663
On the construction of high dimensional simple games
Olsen, Martin; Kurz, Sascha; Molinero Albareda, Xavier
Voting is a commonly applied method for the aggregation
of the preferences of multiple agents into a joint decision. If preferences are binary, i.e., “yes” and “no”, every voting system can be
described by a (monotone) Boolean function : f0; 1gn ! f0; 1g.
However, its naive encoding needs 2n bits. The subclass of threshold
functions, which is sufficient for homogeneous agents, allows
a more succinct representation using n weights and one threshold.
For heterogeneous agents one can represent as an intersection of k
threshold functions. Taylor and Zwicker have constructed a sequence
of examples requiring k 2 n2 ¿1 and provided a construction guaranteeingk ¿ n bn=2c 2 2n¿o(n). The magnitude of the worst case situation was thought to be determined by Elkind et al. in 2008, but the analysis unfortunately turned out to be wrong. Here we uncover a relation to coding theory that allows the determination of the minimum number k for a subclass of voting systems. As an application, we give a construction for k 2n¿o(n), i.e., there is no gain from a representation complexity point of view.
2016-12-01T19:18:00ZOlsen, MartinKurz, SaschaMolinero Albareda, XavierVoting is a commonly applied method for the aggregation
of the preferences of multiple agents into a joint decision. If preferences are binary, i.e., “yes” and “no”, every voting system can be
described by a (monotone) Boolean function : f0; 1gn ! f0; 1g.
However, its naive encoding needs 2n bits. The subclass of threshold
functions, which is sufficient for homogeneous agents, allows
a more succinct representation using n weights and one threshold.
For heterogeneous agents one can represent as an intersection of k
threshold functions. Taylor and Zwicker have constructed a sequence
of examples requiring k 2 n2 ¿1 and provided a construction guaranteeingk ¿ n bn=2c 2 2n¿o(n). The magnitude of the worst case situation was thought to be determined by Elkind et al. in 2008, but the analysis unfortunately turned out to be wrong. Here we uncover a relation to coding theory that allows the determination of the minimum number k for a subclass of voting systems. As an application, we give a construction for k 2n¿o(n), i.e., there is no gain from a representation complexity point of view.Dimension and codimension of simple games
http://hdl.handle.net/2117/97660
Dimension and codimension of simple games
Kurz, Sascha; Molinero Albareda, Xavier; Olsen, Martin; Serna Iglesias, María José
This paper studies the complexity of computing a representation of a simple game as the intersection (union) of weighted majority games, as well as, the dimension or the codimension. We also present some examples with linear dimension and exponential codimension with respect to the number of players.
2016-12-01T18:56:01ZKurz, SaschaMolinero Albareda, XavierOlsen, MartinSerna Iglesias, María JoséThis paper studies the complexity of computing a representation of a simple game as the intersection (union) of weighted majority games, as well as, the dimension or the codimension. We also present some examples with linear dimension and exponential codimension with respect to the number of players.Generic algorithms for the generation of combinatorial objects
http://hdl.handle.net/2117/97031
Generic algorithms for the generation of combinatorial objects
Molinero Albareda, Xavier; Martínez Parra, Conrado
This report briefly describes our generic approach to the exhaustive generation of unlabelled and labelled combinatorial classes. Our algorithms receive a size n and a finite description of a combinatorial class A using combinatorial operators such as union, product, set or sequence, in order to list all objects of size n in A. The algorithms work in constant amortized time per generated object and thus they are suitable for rapid prototyping or for inclusion in general libraries.
2016-11-22T14:37:57ZMolinero Albareda, XavierMartínez Parra, ConradoThis report briefly describes our generic approach to the exhaustive generation of unlabelled and labelled combinatorial classes. Our algorithms receive a size n and a finite description of a combinatorial class A using combinatorial operators such as union, product, set or sequence, in order to list all objects of size n in A. The algorithms work in constant amortized time per generated object and thus they are suitable for rapid prototyping or for inclusion in general libraries.An Efficient generic algorithm for the generation of unlabelled cycles
http://hdl.handle.net/2117/97029
An Efficient generic algorithm for the generation of unlabelled cycles
Martínez Parra, Conrado; Molinero Albareda, Xavier
In this report we combine two recent generation algorithms to obtain a
new algorithm for the generation of unlabelled cycles. Sawada's
algorithm lists all k-ary unlabelled cycles with fixed
content, that is, the
number of occurences of each symbol is fixed and given a priori.
The other algorithm, by the authors, generates all
multisets of objects with given total size n from any admissible
unlabelled class A. By admissible
we mean that the class can be specificied using atomic classes,
disjoints unions, products, sequences, (multi)sets, etc.
The resulting algorithm, which is the main contribution of this paper,
generates all cycles of objects with given total size n from any
admissible class A. Given the
generic nature of the algorithm, it is suitable for inclusion in
combinatorial libraries and for rapid prototyping. The new algorithm
incurs constant amortized time per generated cycle, the constant only
depending in the class A to which the objects in the cycle belong.
2016-11-22T14:33:29ZMartínez Parra, ConradoMolinero Albareda, XavierIn this report we combine two recent generation algorithms to obtain a
new algorithm for the generation of unlabelled cycles. Sawada's
algorithm lists all k-ary unlabelled cycles with fixed
content, that is, the
number of occurences of each symbol is fixed and given a priori.
The other algorithm, by the authors, generates all
multisets of objects with given total size n from any admissible
unlabelled class A. By admissible
we mean that the class can be specificied using atomic classes,
disjoints unions, products, sequences, (multi)sets, etc.
The resulting algorithm, which is the main contribution of this paper,
generates all cycles of objects with given total size n from any
admissible class A. Given the
generic nature of the algorithm, it is suitable for inclusion in
combinatorial libraries and for rapid prototyping. The new algorithm
incurs constant amortized time per generated cycle, the constant only
depending in the class A to which the objects in the cycle belong.Unranking algorithms for combinatorial structures
http://hdl.handle.net/2117/96502
Unranking algorithms for combinatorial structures
Molinero Albareda, Xavier; Vives Pons, Jordi
We present an implementation of some unlabeled and labeled unranking algorithms for the open-source algebraic combinatorics package MUPAD-COMBINAT of the computer algebra system MUPAD. We have compared our implementation with the previous versions. All our algorithms improve the previous ones with respect to the required CPU time. Moreover, we have also developed unranking algorithms applied to some unlabeled and labeled admissible operators that are not still implemented in the package MUPAD-COMBINAT. These algorithms are also able to develop some combinatorial structures useful to generate molecules applied to chemistry and influence graphs applied to game theory and social networks, among other topics.
2016-11-10T18:18:19ZMolinero Albareda, XavierVives Pons, JordiWe present an implementation of some unlabeled and labeled unranking algorithms for the open-source algebraic combinatorics package MUPAD-COMBINAT of the computer algebra system MUPAD. We have compared our implementation with the previous versions. All our algorithms improve the previous ones with respect to the required CPU time. Moreover, we have also developed unranking algorithms applied to some unlabeled and labeled admissible operators that are not still implemented in the package MUPAD-COMBINAT. These algorithms are also able to develop some combinatorial structures useful to generate molecules applied to chemistry and influence graphs applied to game theory and social networks, among other topics.