Ponències/Comunicacions de congressoshttp://hdl.handle.net/2117/34322018-03-18T12:00:17Z2018-03-18T12:00:17ZCombinatorial structures to modeling simple games and applicationsMolinero Albareda, Xavierhttp://hdl.handle.net/2117/1078812017-11-08T11:01:02Z2017-09-21T15:31:46ZCombinatorial structures to modeling simple games and applications
Molinero Albareda, Xavier
We connect three different topics: combinatorial structures, game theory and chemistry. In particular, we establish the bases to represent some simple games, defined as influence games, and molecules, defined from atoms, by using combinatorial structures. First, we characterize simple games as influence games using influence graphs. It let us to modeling simple games as combinatorial structures (from the viewpoint of structures or graphs). Second, we formally define molecules as combinations of atoms. It let us to modeling molecules as combinatorial structures (from the viewpoint of combinations). It is open to generate such combinatorial structures using some specific techniques as genetic algorithms, (meta-)heuristics algorithms and parallel programming, among others.
2017-09-21T15:31:46ZMolinero Albareda, XavierWe connect three different topics: combinatorial structures, game theory and chemistry. In particular, we establish the bases to represent some simple games, defined as influence games, and molecules, defined from atoms, by using combinatorial structures. First, we characterize simple games as influence games using influence graphs. It let us to modeling simple games as combinatorial structures (from the viewpoint of structures or graphs). Second, we formally define molecules as combinations of atoms. It let us to modeling molecules as combinatorial structures (from the viewpoint of combinations). It is open to generate such combinatorial structures using some specific techniques as genetic algorithms, (meta-)heuristics algorithms and parallel programming, among others.Ability to separate situations with a priori coalition structures by means of symmetric solutionsGiménez Pradales, José Miguelhttp://hdl.handle.net/2117/1025172017-11-08T11:01:02Z2017-03-15T13:33:58ZAbility 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.A new procedure to calculate the Owen valuePuente del Campo, María AlbinaGiménez Pradales, José Miguelhttp://hdl.handle.net/2117/1022502017-03-15T13:23:44Z2017-03-09T19:07:48ZA 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.On the construction of high dimensional simple gamesOlsen, MartinKurz, SaschaMolinero Albareda, Xavierhttp://hdl.handle.net/2117/976632017-11-08T11:01:02Z2016-12-01T19:18:00ZOn 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.Components with higher and lower risk in a reliability systemFreixas Bosch, JosepPons Vallès, Montserrathttp://hdl.handle.net/2117/841792017-11-08T11:01:07Z2016-03-10T19:15:02ZComponents with higher and lower risk in a reliability system
Freixas Bosch, Josep; Pons Vallès, Montserrat
A new reliability importance measure for components in a system, that we
call Representativeness measure, is introduced. It evaluates to which extent the performance of a component is representative of the erformance of the whole system. Its relationship with Birnbaum’s measure is analyzed, and the ranking of components given by both measures are compared. These rankings happen to be equal when all components have the same reliability but different in general. In contrast with Birnbaum’s, the Representativeness reliability importance measure of a component does depend on its reliability.
2016-03-10T19:15:02ZFreixas Bosch, JosepPons Vallès, MontserratA new reliability importance measure for components in a system, that we
call Representativeness measure, is introduced. It evaluates to which extent the performance of a component is representative of the erformance of the whole system. Its relationship with Birnbaum’s measure is analyzed, and the ranking of components given by both measures are compared. These rankings happen to be equal when all components have the same reliability but different in general. In contrast with Birnbaum’s, the Representativeness reliability importance measure of a component does depend on its reliability.Computational procedure for a wide family of mixed coalitional valuesGiménez Pradales, José MiguelPuente del Campo, María Albinahttp://hdl.handle.net/2117/785332015-11-17T12:56:35Z2015-10-29T18:11:54ZComputational procedure for a wide family of mixed coalitional values
Giménez Pradales, José Miguel; Puente del Campo, María Albina
We consider a family of mixed coalitional values. They apply to games with a coalition structure by combining a (induced) semivalue in the quotient game, but share within each union the payoff so obtained by applying different (induced) semivalues to a game that concerns only the players of that union. A computation procedure in terms of the multilinear extension of the original game is provided.
2015-10-29T18:11:54ZGiménez Pradales, José MiguelPuente del Campo, María AlbinaWe consider a family of mixed coalitional values. They apply to games with a coalition structure by combining a (induced) semivalue in the quotient game, but share within each union the payoff so obtained by applying different (induced) semivalues to a game that concerns only the players of that union. A computation procedure in terms of the multilinear extension of the original game is provided.Similarities and differences between success and decisivenessFreixas Bosch, JosepPons Vallès, Montserrathttp://hdl.handle.net/2117/245682017-02-12T09:07:32Z2014-11-05T14:51:09ZSimilarities and differences between success and decisiveness
Freixas Bosch, Josep; Pons Vallès, Montserrat
We consider binary voting systems in which a probability distribution
over coalitions is known. In this broader context decisiveness is
an extension of the Penrose-Banzhaf index and success an extension of the Rae index for simple games. Although decisiveness and success are conceptually different we analyze their numerical behavior. The main result provides necessary and sufficient conditions for the ordinal equivalence of them. Indeed, under anonymous probability distributions they become ordinally equivalent. Moreover, it is proved that for these distributions, decisiveness and success respect the strength of the seats, whereas luckiness reverses the order.
2014-11-05T14:51:09ZFreixas Bosch, JosepPons Vallès, MontserratWe consider binary voting systems in which a probability distribution
over coalitions is known. In this broader context decisiveness is
an extension of the Penrose-Banzhaf index and success an extension of the Rae index for simple games. Although decisiveness and success are conceptually different we analyze their numerical behavior. The main result provides necessary and sufficient conditions for the ordinal equivalence of them. Indeed, under anonymous probability distributions they become ordinally equivalent. Moreover, it is proved that for these distributions, decisiveness and success respect the strength of the seats, whereas luckiness reverses the order.The representativeness reliability importance measureFreixas Bosch, JosepPons Vallès, Montserrathttp://hdl.handle.net/2117/240482017-02-12T06:28:45Z2014-09-12T10:45:20ZThe representativeness reliability importance measure
Freixas Bosch, Josep; Pons Vallès, Montserrat
A new reliability importance measure for
components in a system, that we call Representativeness
measure, is introduced. It evaluates to which extent the
performance of a component is representative of the
performance of the whole system. Its relationship with
Birnbaum’s measure is analyzed, and the ranking of
components given by both measures are compared. These
rankings happen to be equal when all components have the
same reliability but different in general. In contrast with
Birnbaum’s, the Representativeness reliability importance
measure of a component does depend on its reliability.
2014-09-12T10:45:20ZFreixas Bosch, JosepPons Vallès, MontserratA new reliability importance measure for
components in a system, that we call Representativeness
measure, is introduced. It evaluates to which extent the
performance of a component is representative of the
performance of the whole system. Its relationship with
Birnbaum’s measure is analyzed, and the ranking of
components given by both measures are compared. These
rankings happen to be equal when all components have the
same reliability but different in general. In contrast with
Birnbaum’s, the Representativeness reliability importance
measure of a component does depend on its reliability.Cooperation tendencies and evaluation of gamesCarreras Escobar, FranciscoPuente del Campo, María Albinahttp://hdl.handle.net/2117/205342017-02-11T11:30:08Z2013-11-05T19:13:56ZCooperation tendencies and evaluation of games
Carreras Escobar, Francisco; Puente del Campo, María Albina
Multinomial probabilistic values were first introduced by one of us in reliability and later on by the other,
independently, as power indices. Here we study them on cooperative games from several viewpoints, and especially
as a powerful generalization of binomial semivalues. We establish a dimensional comparison between
multinomial values and binomial semivalues and provide two characterizations within the class of probabilistic
values: one for each multinomial value and another for the whole family. An example illustrates their use
in practice as power indices.
2013-11-05T19:13:56ZCarreras Escobar, FranciscoPuente del Campo, María AlbinaMultinomial probabilistic values were first introduced by one of us in reliability and later on by the other,
independently, as power indices. Here we study them on cooperative games from several viewpoints, and especially
as a powerful generalization of binomial semivalues. We establish a dimensional comparison between
multinomial values and binomial semivalues and provide two characterizations within the class of probabilistic
values: one for each multinomial value and another for the whole family. An example illustrates their use
in practice as power indices.Nodes of directed graphs ranked by solutions defined on cooperative gamesAmer Ramon, RafaelGiménez Pradales, José MiguelMagaña Nieto, Antoniohttp://hdl.handle.net/2117/104912017-02-06T11:23:14Z2010-12-02T15:26:30ZNodes of directed graphs ranked by solutions defined on cooperative games
Amer Ramon, Rafael; Giménez Pradales, José Miguel; Magaña Nieto, Antonio
Hierarchical structures, transportation systems, communication networks and
even sports competitions can be modeled by means of directed graphs. Since
digraphs without a predefined game are considered, the main part of the work is
devoted to establish conditions on cooperative games so that they can be used
to measure accessibility to the nodes. Games that satisfy desirable properties
are called test games. Each ranking on the nodes is then obtained according
to a pair formed by a test game and a solution defined on cooperative games
whose utilities are given for every ordered coalition. Solutions here proposed
are extensions of the wide family of semivalues to games in generalized characteristic
function form.
2010-12-02T15:26:30ZAmer Ramon, RafaelGiménez Pradales, José MiguelMagaña Nieto, AntonioHierarchical structures, transportation systems, communication networks and
even sports competitions can be modeled by means of directed graphs. Since
digraphs without a predefined game are considered, the main part of the work is
devoted to establish conditions on cooperative games so that they can be used
to measure accessibility to the nodes. Games that satisfy desirable properties
are called test games. Each ranking on the nodes is then obtained according
to a pair formed by a test game and a solution defined on cooperative games
whose utilities are given for every ordered coalition. Solutions here proposed
are extensions of the wide family of semivalues to games in generalized characteristic
function form.