GRTJ - Grup de Recerca en Teoria de Jocs
http://hdl.handle.net/2117/3429
Thu, 08 Dec 2016 08:20:05 GMT2016-12-08T08:20:05ZOn 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.
Thu, 01 Dec 2016 19:18:00 GMThttp://hdl.handle.net/2117/976632016-12-01T19:18:00ZOlsen, 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.
Thu, 01 Dec 2016 18:56:01 GMThttp://hdl.handle.net/2117/976602016-12-01T18:56:01ZKurz, 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.
Tue, 22 Nov 2016 14:37:57 GMThttp://hdl.handle.net/2117/970312016-11-22T14:37:57ZMolinero 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.
Tue, 22 Nov 2016 14:33:29 GMThttp://hdl.handle.net/2117/970292016-11-22T14:33:29ZMartínez 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.
Thu, 10 Nov 2016 18:18:19 GMThttp://hdl.handle.net/2117/965022016-11-10T18:18:19ZMolinero 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.The complexity of measuring power in generalized opinion leader decision models
http://hdl.handle.net/2117/91242
The complexity of measuring power in generalized opinion leader decision models
Molinero Albareda, Xavier; Serna Iglesias, María José
We analyze the computational complexity of the power measure in models of collective decision: the generalized opinion leader-follower model and the oblivious and non-oblivious infuence models. We show that computing the power measure is #P-hard in all these models, and provide two subfamilies in which the power measure can be computed in polynomial time.
Fri, 28 Oct 2016 16:03:04 GMThttp://hdl.handle.net/2117/912422016-10-28T16:03:04ZMolinero Albareda, XavierSerna Iglesias, María JoséWe analyze the computational complexity of the power measure in models of collective decision: the generalized opinion leader-follower model and the oblivious and non-oblivious infuence models. We show that computing the power measure is #P-hard in all these models, and provide two subfamilies in which the power measure can be computed in polynomial time.Dimension, egalitarianism and decisiveness of European voting systems
http://hdl.handle.net/2117/91241
Dimension, egalitarianism and decisiveness of European voting systems
Carreras Escobar, Francisco; Freixas Bosch, Josep; Magaña Nieto, Antonio
An analysis of three major aspects has been carried out that may apply to any of the successive voting systems used for the European Union Council of Ministers, from the first one established in the Treaty of Rome in 1958 to the current one established in Lisbon. We mainly consider the voting systems designed for the enlarged European Union adopted in the Athens summit, held in April 2003 but this analysis can be applied to any other system. First, it is shown that the dimension of these voting systems does not, in general, reduce. Next, the egalitarian effects of superposing two or three weighted majority games (often by introducing additional consensus) are considered. Finally, the decisiveness of these voting systems is evaluated and compared.
Fri, 28 Oct 2016 15:46:31 GMThttp://hdl.handle.net/2117/912412016-10-28T15:46:31ZCarreras Escobar, FranciscoFreixas Bosch, JosepMagaña Nieto, AntonioAn analysis of three major aspects has been carried out that may apply to any of the successive voting systems used for the European Union Council of Ministers, from the first one established in the Treaty of Rome in 1958 to the current one established in Lisbon. We mainly consider the voting systems designed for the enlarged European Union adopted in the Athens summit, held in April 2003 but this analysis can be applied to any other system. First, it is shown that the dimension of these voting systems does not, in general, reduce. Next, the egalitarian effects of superposing two or three weighted majority games (often by introducing additional consensus) are considered. Finally, the decisiveness of these voting systems is evaluated and compared.Pure bargaining problems with a coalition structure
http://hdl.handle.net/2117/89737
Pure bargaining problems with a coalition structure
Carreras Escobar, Francisco; Owen Salazar, Guillermo
We consider here pure bargaining problems endowed with a coalition structure such that each union is given its own utility. In this context we use the Shapley rule in order to assess the main options available to the agents: individual behavior, cooperative behavior, isolated unions behavior, and bargaining unions behavior. The latter two respectively recall the treatment given by Aumann–Drèze and Owen to cooperative games with a coalition structure. A numerical example illustrates the procedure. We provide criteria to compare any pair of behaviors for each agent, introduce and axiomatically characterize a modified Shapley rule, and determine its natural domain, that is, the set of problems where the bargaining unions behavior is the best option for all agents.
The final publication is available at Springer via http://dx.doi.org/10.1007/s41412-016-0007-2
Thu, 08 Sep 2016 11:00:25 GMThttp://hdl.handle.net/2117/897372016-09-08T11:00:25ZCarreras Escobar, FranciscoOwen Salazar, GuillermoWe consider here pure bargaining problems endowed with a coalition structure such that each union is given its own utility. In this context we use the Shapley rule in order to assess the main options available to the agents: individual behavior, cooperative behavior, isolated unions behavior, and bargaining unions behavior. The latter two respectively recall the treatment given by Aumann–Drèze and Owen to cooperative games with a coalition structure. A numerical example illustrates the procedure. We provide criteria to compare any pair of behaviors for each agent, introduce and axiomatically characterize a modified Shapley rule, and determine its natural domain, that is, the set of problems where the bargaining unions behavior is the best option for all agents.On the time decay of solutions for non-simple elasticity with voids
http://hdl.handle.net/2117/89329
On the time decay of solutions for non-simple elasticity with voids
Liu, Zhuangyi; Magaña Nieto, Antonio; Quintanilla de Latorre, Ramón
In this work we consider the non-simple theory of elastic material with voids and we investigate how the coupling of these two aspects of the material affects the behavior of the solutions. We analyze only two kind of different behavior, slow or exponential decay. We introduce four different dissipation mechanisms in the system and we study, in each case, the effect of this mechanism in the behavior of the solutions.
Thu, 28 Jul 2016 11:25:42 GMThttp://hdl.handle.net/2117/893292016-07-28T11:25:42ZLiu, ZhuangyiMagaña Nieto, AntonioQuintanilla de Latorre, RamónIn this work we consider the non-simple theory of elastic material with voids and we investigate how the coupling of these two aspects of the material affects the behavior of the solutions. We analyze only two kind of different behavior, slow or exponential decay. We introduce four different dissipation mechanisms in the system and we study, in each case, the effect of this mechanism in the behavior of the solutions.Decisiveness indices are semiindices
http://hdl.handle.net/2117/89036
Decisiveness indices are semiindices
Freixas Bosch, Josep; Pons Vallès, Montserrat
In this note we prove that any decisiveness index, defined for any voter as the probability of him/her being decisive, is a semiindex when the probability distribution over coalitions is anonymous, and it is a semiindex with binomial coefficients when the probability over coalitions is anonymous and independent.
Thu, 21 Jul 2016 11:26:45 GMThttp://hdl.handle.net/2117/890362016-07-21T11:26:45ZFreixas Bosch, JosepPons Vallès, MontserratIn this note we prove that any decisiveness index, defined for any voter as the probability of him/her being decisive, is a semiindex when the probability distribution over coalitions is anonymous, and it is a semiindex with binomial coefficients when the probability over coalitions is anonymous and independent.