GRTJ - Grup de Recerca en Teoria de Jocs
http://hdl.handle.net/2117/3429
Sun, 01 May 2016 19:32:56 GMT2016-05-01T19:32:56ZMinimal representations for majority games
http://hdl.handle.net/2117/86215
Minimal representations for majority games
Freixas Bosch, Josep; Molinero Albareda, Xavier; Roura Ferret, Salvador
This paper presents some new results about majority games. Isbell (1959) was the first to find a majority game without a minimum normalized representation; he needed 12 voters to construct such a game. Since then, it has been an open problem to find the minimum number of voters of a majority game without a minimum normalized representation. Our main new results are: 1. All majority games with less than 9 voters have a minimum representation. 2. For 9 voters there are 14 majority games without a minimum integer representation, but these games admit a minimal normalized integer representation. 3. For 10 voters exist majority games with neither a minimum integer representation nor a minimal normalized integer representation.
Wed, 27 Apr 2016 07:22:54 GMThttp://hdl.handle.net/2117/862152016-04-27T07:22:54ZFreixas Bosch, JosepMolinero Albareda, XavierRoura Ferret, SalvadorThis paper presents some new results about majority games. Isbell (1959) was the first to find a majority game without a minimum normalized representation; he needed 12 voters to construct such a game. Since then, it has been an open problem to find the minimum number of voters of a majority game without a minimum normalized representation. Our main new results are: 1. All majority games with less than 9 voters have a minimum representation. 2. For 9 voters there are 14 majority games without a minimum integer representation, but these games admit a minimal normalized integer representation. 3. For 10 voters exist majority games with neither a minimum integer representation nor a minimal normalized integer representation.On the complexity of exchanging
http://hdl.handle.net/2117/86068
On the complexity of exchanging
Molinero Albareda, Xavier; Olsen, Martin; Serna Iglesias, María José
We analyze the computational complexity of the problem of deciding whether, for a given simple game, there exists the possibility of rearranging the participants in a set of j given losing coalitions into a set of j winning coalitions. We also look at the problem of turning winning coalitions into losing coalitions. We analyze the problem when the simple game is represented by a list of wining, losing, minimal winning or maximal loosing coalitions.
Thu, 21 Apr 2016 13:57:53 GMThttp://hdl.handle.net/2117/860682016-04-21T13:57:53ZMolinero Albareda, XavierOlsen, MartinSerna Iglesias, María JoséWe analyze the computational complexity of the problem of deciding whether, for a given simple game, there exists the possibility of rearranging the participants in a set of j given losing coalitions into a set of j winning coalitions. We also look at the problem of turning winning coalitions into losing coalitions. We analyze the problem when the simple game is represented by a list of wining, losing, minimal winning or maximal loosing coalitions.Components with higher and lower risk in a reliability system
http://hdl.handle.net/2117/84179
Components 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.
Thu, 10 Mar 2016 19:15:02 GMThttp://hdl.handle.net/2117/841792016-03-10T19:15:02ZFreixas 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.Power in voting rules with abstention: an axiomatization of a two components power index
http://hdl.handle.net/2117/84162
Power in voting rules with abstention: an axiomatization of a two components power index
Freixas Bosch, Josep; Lucchetti, Roberto
In order to study voting situations when voters can also abstain and the output is binary, i.e., either approval or rejection, a new extended model of voting rule was defined. Accordingly, indices of power, in particular Banzhaf’s index, were considered. In this paper we argue that in this context a power index should be a pair of real numbers, since this better highlights the power of a voter in two different cases, i.e., her being crucial when switching from being in favor to abstain, and from abstain to be contrary. We also provide an axiomatization for both indices, and from this a characterization as well of the standard Banzhaf index (the sum of the former two) is obtained. Some examples are provided to show how the indices behave.
The final publication is available at Springer via http://dx.doi.org/10.1007/s10479-016-2124-5
Thu, 10 Mar 2016 15:58:37 GMThttp://hdl.handle.net/2117/841622016-03-10T15:58:37ZFreixas Bosch, JosepLucchetti, RobertoIn order to study voting situations when voters can also abstain and the output is binary, i.e., either approval or rejection, a new extended model of voting rule was defined. Accordingly, indices of power, in particular Banzhaf’s index, were considered. In this paper we argue that in this context a power index should be a pair of real numbers, since this better highlights the power of a voter in two different cases, i.e., her being crucial when switching from being in favor to abstain, and from abstain to be contrary. We also provide an axiomatization for both indices, and from this a characterization as well of the standard Banzhaf index (the sum of the former two) is obtained. Some examples are provided to show how the indices behave.Exponential decay in nonsimple thermoelasticity of type III
http://hdl.handle.net/2117/83497
Exponential decay in nonsimple thermoelasticity of type III
Magaña Nieto, Antonio; Quintanilla de Latorre, Ramón
This paper deals with the model proposed for nonsimple materials
with heat conduction of type III.We analyze rst the general system of equations, determine the behavior of its solutions with respect to the time and show that the semigroup associated with the system is not analytic. Two limiting cases of the model are studied later.
This is the peer reviewed version of the following article: Magaña, A., and Quintanilla, R. (2016) Exponential decay in nonsimple thermoelasticity of type III. Math. Meth. Appl. Sci., 39: 225–235. doi: 10.1002/mma.3472, which has been published in final form at http://dx.doi.org/10.1002/mma.3472. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving
Fri, 26 Feb 2016 13:13:35 GMThttp://hdl.handle.net/2117/834972016-02-26T13:13:35ZMagaña Nieto, AntonioQuintanilla de Latorre, RamónThis paper deals with the model proposed for nonsimple materials
with heat conduction of type III.We analyze rst the general system of equations, determine the behavior of its solutions with respect to the time and show that the semigroup associated with the system is not analytic. Two limiting cases of the model are studied later.Manipulation in games with multiple levels of output
http://hdl.handle.net/2117/80825
Manipulation in games with multiple levels of output
Freixas Bosch, Josep; Parker, Cameron
In (j,k)-games each player chooses amongst j ordered options and there are k possible outcomes. In this paper, we consider the case where players are assumed to prefer some outcomes to others, and note that when k>2 the players have an incentive to vote strategically. In doing so, we combine the theory of cooperative game theory with social choice theory, especially the theory of single-peaked preferences. We define the concept of a (j,k)-game with preferences and what it means for it to be manipulable by a player. We also consider Nash equilibriums with pure strategies for these games and find conditions that guarantee their existence.
Wed, 16 Dec 2015 16:44:35 GMThttp://hdl.handle.net/2117/808252015-12-16T16:44:35ZFreixas Bosch, JosepParker, CameronIn (j,k)-games each player chooses amongst j ordered options and there are k possible outcomes. In this paper, we consider the case where players are assumed to prefer some outcomes to others, and note that when k>2 the players have an incentive to vote strategically. In doing so, we combine the theory of cooperative game theory with social choice theory, especially the theory of single-peaked preferences. We define the concept of a (j,k)-game with preferences and what it means for it to be manipulable by a player. We also consider Nash equilibriums with pure strategies for these games and find conditions that guarantee their existence.A method to calculate generalized mixed modified semivalues: application to the Catalan Parliament (legislature 2012-2016)
http://hdl.handle.net/2117/80018
A method to calculate generalized mixed modified semivalues: application to the Catalan Parliament (legislature 2012-2016)
Giménez Pradales, José Miguel; Puente del Campo, María Albina
We focus on generalized mixed modified semivalues, a family of 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 also provided and an application to the Catalan Parliament (legislature 2012-2016) is shown
The final publication is available at Springer via http://dx.doi.org/10.1007/s11750-014-0356-6”.
Fri, 27 Nov 2015 16:23:44 GMThttp://hdl.handle.net/2117/800182015-11-27T16:23:44ZGiménez Pradales, José MiguelPuente del Campo, María AlbinaWe focus on generalized mixed modified semivalues, a family of 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 also provided and an application to the Catalan Parliament (legislature 2012-2016) is shownIdentifying optimal components in a reliability system
http://hdl.handle.net/2117/78945
Identifying optimal components in a reliability system
Freixas Bosch, Josep; Pons Vallès, Montserrat
The first step in a reliability optimization process is to
make a reliability assessment for each component in the system. If
this assessment is made in a qualitative way, by grouping together
components with the same reliability, and establishing a prevalence
order among groups, is there a way to decide which components
have the greatest Birnbaum measure without computing the exact
value of this measure? In this paper, three relations between com-
ponents are introduced and studied, and it is proved that they are
useful for selecting the components that have the biggest effect on
the system reliability in the sense of Birnbaum. An algorithm that
uses the results in the paper to select these important components
is also provided.
Mon, 09 Nov 2015 17:12:18 GMThttp://hdl.handle.net/2117/789452015-11-09T17:12:18ZFreixas Bosch, JosepPons Vallès, MontserratThe first step in a reliability optimization process is to
make a reliability assessment for each component in the system. If
this assessment is made in a qualitative way, by grouping together
components with the same reliability, and establishing a prevalence
order among groups, is there a way to decide which components
have the greatest Birnbaum measure without computing the exact
value of this measure? In this paper, three relations between com-
ponents are introduced and studied, and it is proved that they are
useful for selecting the components that have the biggest effect on
the system reliability in the sense of Birnbaum. An algorithm that
uses the results in the paper to select these important components
is also provided.Multinomial probabilistic values
http://hdl.handle.net/2117/78579
Multinomial probabilistic values
Carreras Escobar, Francisco; Puente del Campo, María Albina
Multinomial probabilistic values were introduced by one of us in reliability. Here we define them for all cooperative games and illustrate their behavior in practice by means of an application to the analysis of a political problem.
Fri, 30 Oct 2015 18:15:01 GMThttp://hdl.handle.net/2117/785792015-10-30T18:15:01ZCarreras Escobar, FranciscoPuente del Campo, María AlbinaMultinomial probabilistic values were introduced by one of us in reliability. Here we define them for all cooperative games and illustrate their behavior in practice by means of an application to the analysis of a political problem.Computational procedure for a wide family of mixed coalitional values
http://hdl.handle.net/2117/78533
Computational 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.
Thu, 29 Oct 2015 18:11:54 GMThttp://hdl.handle.net/2117/785332015-10-29T18:11:54ZGiménez 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.