DSpace Community:
http://hdl.handle.net/2117/3429
Mon, 21 Apr 2014 00:49:52 GMT2014-04-21T00:49:52Zwebmaster.bupc@upc.eduUniversitat Politècnica de Catalunya. Servei de Biblioteques i DocumentaciónoOn the uniqueness and analyticity of solutions in micropolar thermoviscoelasticity
http://hdl.handle.net/2117/21495
Title: On the uniqueness and analyticity of solutions in micropolar thermoviscoelasticity
Authors: Magaña Nieto, Antonio; Quintanilla de Latorre, Ramón
Abstract: This paper deals with the linear theory of isotropic micropolar thermoviscoelastic materials. When the dissipation is positive definite, we present two uniqueness theorems. The first one requires the extra assumption that some coupling terms vanish; in this case, the instability of solutions is also proved. When the internal energy and the dissipation are both positive definite, we prove the well-posedness of the problem and the analyticity of the solutions. Exponential decay and impossibility of localization are corollaries of the analyticity.Mon, 10 Feb 2014 14:06:59 GMThttp://hdl.handle.net/2117/214952014-02-10T14:06:59ZMagaña Nieto, Antonio; Quintanilla de Latorre, RamónnoMicropolar thermoviscoelasticity, Uniqueness, Analyticity, Exponential decayThis paper deals with the linear theory of isotropic micropolar thermoviscoelastic materials. When the dissipation is positive definite, we present two uniqueness theorems. The first one requires the extra assumption that some coupling terms vanish; in this case, the instability of solutions is also proved. When the internal energy and the dissipation are both positive definite, we prove the well-posedness of the problem and the analyticity of the solutions. Exponential decay and impossibility of localization are corollaries of the analyticity.The minimum sum representation as an index of voting power
http://hdl.handle.net/2117/21411
Title: The minimum sum representation as an index of voting power
Authors: Freixas Bosch, Josep; Kaniovski, Serguei
Abstract: We propose a new power index based on the minimum sum representation (MSR) of a
weighted voting game. The MSR o ers a redesign of a voting game, such that voting power
as measured by the MSR index becomes proportional to voting weight. The MSR index is a
coherent measure of power that is ordinally equivalent to the Banzhaf, Shapley-Shubik and
Johnston indices. We provide a characterization for a bicameral meet as a weighted game or
a complete game, and show that the MSR index is immune to the bicameral meet paradox.
We discuss the computation of the MSR index using a linear integer program and the inverse MSR problem of designing a weighted voting game with a given distribution of power.Thu, 30 Jan 2014 19:11:23 GMThttp://hdl.handle.net/2117/214112014-01-30T19:11:23ZFreixas Bosch, Josep; Kaniovski, SergueinoBicameral meet, Minimum integer sum representation, Power indices, Proportional design between shares and power, RankingsWe propose a new power index based on the minimum sum representation (MSR) of a
weighted voting game. The MSR o ers a redesign of a voting game, such that voting power
as measured by the MSR index becomes proportional to voting weight. The MSR index is a
coherent measure of power that is ordinally equivalent to the Banzhaf, Shapley-Shubik and
Johnston indices. We provide a characterization for a bicameral meet as a weighted game or
a complete game, and show that the MSR index is immune to the bicameral meet paradox.
We discuss the computation of the MSR index using a linear integer program and the inverse MSR problem of designing a weighted voting game with a given distribution of power.Reconstructing a simple game from a uniparametric family of allocations
http://hdl.handle.net/2117/20914
Title: Reconstructing a simple game from a uniparametric family of allocations
Authors: Amer Ramon, Rafael; Giménez Pradales, José Miguel; Magaña Nieto, Antonio
Abstract: Several relationships between simple games and a particular type of solu-
tions for cooperative games are studied in this paper. These solutions belong to the
set of semivalues and they are related to a unique parameter that explicitly provides
their weighting coefficients. Through the allocations offered by this family of solu-
tions, so-called binomial semivalues, and also from their respective potentials, some
characteristics of the simple games can be recovered. The paper analyzes the capacity
of binomial semivalues to summarize the structure of simple games, and, moreover,
a property of separation among simple games is given.Wed, 04 Dec 2013 16:00:12 GMThttp://hdl.handle.net/2117/209142013-12-04T16:00:12ZAmer Ramon, Rafael; Giménez Pradales, José Miguel; Magaña Nieto, AntonionoBanzhaf value, Game theory, Potential, Semivalue, Simple gameSeveral relationships between simple games and a particular type of solu-
tions for cooperative games are studied in this paper. These solutions belong to the
set of semivalues and they are related to a unique parameter that explicitly provides
their weighting coefficients. Through the allocations offered by this family of solu-
tions, so-called binomial semivalues, and also from their respective potentials, some
characteristics of the simple games can be recovered. The paper analyzes the capacity
of binomial semivalues to summarize the structure of simple games, and, moreover,
a property of separation among simple games is given.Cooperation tendencies and evaluation of games
http://hdl.handle.net/2117/20534
Title: Cooperation tendencies and evaluation of games
Authors: Carreras Escobar, Francisco; Puente del Campo, María Albina
Abstract: 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.Tue, 05 Nov 2013 19:13:56 GMThttp://hdl.handle.net/2117/205342013-11-05T19:13:56ZCarreras Escobar, Francisco; Puente del Campo, María AlbinanoCooperative game, Shapley value, Probabilistic value, Binomial semivalueMultinomial 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.Computation of several power indices by generating functions
http://hdl.handle.net/2117/17925
Title: Computation of several power indices by generating functions
Authors: Alonso Meijide, José María; Freixas Bosch, Josep; Molinero Albareda, Xavier
Abstract: In this paper we propose methods to compute the Deegan-Packel, the Public
Good, and the Shift power indices by generating functions for the particular
case of weighted voting games. Furthermore, we define a new power index
which combines the ideas of the Shift and the Deegan-Packel power indices and
also propose a method to compute it with generating functions. We conclude
by some comments about the complexity to compute these power indices.Fri, 22 Feb 2013 10:25:06 GMThttp://hdl.handle.net/2117/179252013-02-22T10:25:06ZAlonso Meijide, José María; Freixas Bosch, Josep; Molinero Albareda, XaviernoIn this paper we propose methods to compute the Deegan-Packel, the Public
Good, and the Shift power indices by generating functions for the particular
case of weighted voting games. Furthermore, we define a new power index
which combines the ideas of the Shift and the Deegan-Packel power indices and
also propose a method to compute it with generating functions. We conclude
by some comments about the complexity to compute these power indices.Pure bargaining problems and the Shapley rule
http://hdl.handle.net/2117/16208
Title: Pure bargaining problems and the Shapley rule
Authors: Carreras Escobar, Francisco; Owen Salazar, Guillermo
Abstract: Pure bargaining problems with transferable utility are considered. By associating a quasi-additive cooperative game with each one of them, a Shapley rule for this class of problems is derived from the Shapley value for games. The analysis of this new rule includes axiomatic characterizations and a comparison with the proportional rule.Mon, 09 Jul 2012 11:56:32 GMThttp://hdl.handle.net/2117/162082012-07-09T11:56:32ZCarreras Escobar, Francisco; Owen Salazar, GuillermonoPure bargaining problems with transferable utility are considered. By associating a quasi-additive cooperative game with each one of them, a Shapley rule for this class of problems is derived from the Shapley value for games. The analysis of this new rule includes axiomatic characterizations and a comparison with the proportional rule.Accessibility measures to nodes of directed graphs using solutions for generalized cooperative games
http://hdl.handle.net/2117/16206
Title: Accessibility measures to nodes of directed graphs using solutions for generalized cooperative games
Authors: Amer Ramon, Rafael; Giménez Pradales, José Miguel; Magaña Nieto, Antonio
Abstract: The aim of this paper consists of constructing accessibility measures to
the nodes of directed graphs using methods of Game Theory. Since digraphs without a
predefined game are considered, the main part of the paper is devoted to establish conditions
on cooperative games so that they can be used to measure accessibility. 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 on ordered coalitions. The solutions proposed
here are extensions of the wide family of semivalues to games in generalized
characteristic function form.Mon, 09 Jul 2012 11:34:13 GMThttp://hdl.handle.net/2117/162062012-07-09T11:34:13ZAmer Ramon, Rafael; Giménez Pradales, José Miguel; Magaña Nieto, AntonionoGame theory, Digraph, Accessibility, Cooperative game, SemivalueThe aim of this paper consists of constructing accessibility measures to
the nodes of directed graphs using methods of Game Theory. Since digraphs without a
predefined game are considered, the main part of the paper is devoted to establish conditions
on cooperative games so that they can be used to measure accessibility. 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 on ordered coalitions. The solutions proposed
here are extensions of the wide family of semivalues to games in generalized
characteristic function form.Complete voting systems with two types of voters: weightedness and counting
http://hdl.handle.net/2117/16145
Title: Complete voting systems with two types of voters: weightedness and counting
Authors: Freixas Bosch, Josep; Molinero Albareda, Xavier; Roura Ferret, Salvador
Abstract: We investigate voting systems with two classes of voters, for which there is a hierarchy giving each member of the stronger class more influence or important than each member of the weaker class. We deduce for voting systems one important counting fact that allows determining how many of them are for a given number of voters. In fact, the number of these systems follows a Fibonacci sequence with a smooth polynomial variation on the number of voters. On the other hand, we classify by means of some parameters which of these systems are weighted. This result allows us to state an asymptotic conjecture which is opposed to what occurs for symmetric games.Wed, 27 Jun 2012 12:59:15 GMThttp://hdl.handle.net/2117/161452012-06-27T12:59:15ZFreixas Bosch, Josep; Molinero Albareda, Xavier; Roura Ferret, SalvadornoWe investigate voting systems with two classes of voters, for which there is a hierarchy giving each member of the stronger class more influence or important than each member of the weaker class. We deduce for voting systems one important counting fact that allows determining how many of them are for a given number of voters. In fact, the number of these systems follows a Fibonacci sequence with a smooth polynomial variation on the number of voters. On the other hand, we classify by means of some parameters which of these systems are weighted. This result allows us to state an asymptotic conjecture which is opposed to what occurs for symmetric games.Probabilistic power indices for voting rules with abstention
http://hdl.handle.net/2117/16144
Title: Probabilistic power indices for voting rules with abstention
Authors: Freixas Bosch, Josep
Abstract: In this paper, we introduce eight power indices that admit a probabilistic interpretation for voting rules with abstention or with three levels of approval in the input, briefly (3, 2) games.Weanalyze the analogies and discrepancies between standard known indices for simple games and the proposed extensions for this more general context. A remarkable difference is that for (3, 2) games the proposed extensions of the Banzhaf index, Coleman index to prevent action and Coleman index to initiate action become non-proportional
notions, contrarily to what succeeds for simple games. We conclude the work by providing procedures based on generating functions for weighted (3, 2) games, and extensible to (j,k) games, to efficiently compute them.Wed, 27 Jun 2012 12:46:37 GMThttp://hdl.handle.net/2117/161442012-06-27T12:46:37ZFreixas Bosch, JosepnoIn this paper, we introduce eight power indices that admit a probabilistic interpretation for voting rules with abstention or with three levels of approval in the input, briefly (3, 2) games.Weanalyze the analogies and discrepancies between standard known indices for simple games and the proposed extensions for this more general context. A remarkable difference is that for (3, 2) games the proposed extensions of the Banzhaf index, Coleman index to prevent action and Coleman index to initiate action become non-proportional
notions, contrarily to what succeeds for simple games. We conclude the work by providing procedures based on generating functions for weighted (3, 2) games, and extensible to (j,k) games, to efficiently compute them.A note on decisive symmetric games
http://hdl.handle.net/2117/13512
Title: A note on decisive symmetric games
Authors: Carreras Escobar, Francisco; Freixas Bosch, Josep; Puente del Campo, María Albina
Abstract: Binary voting systems, usually represented by simple games, constitute a main DSS topic. A crucial feature of
such a system is the easiness with which a proposal can be collectively accepted, which is measured by the
“decisiveness index” of the corresponding game. We study here several functions related to the decisiveness
of any simple game. The analysis, including the asymptotic behavior as the number n of players increases, is
restricted to decisive symmetric games and their compositions, and it is assumed that all players have a
common probability p to vote for the proposal. We show that, for n large enough, a small variation, either
positive or negative, in p when p=1/2 takes the decisiveness to quickly approach, respectively, 1 or 0.
Moreover, we analyze the speed of the decisiveness convergence.Fri, 14 Oct 2011 16:58:43 GMThttp://hdl.handle.net/2117/135122011-10-14T16:58:43ZCarreras Escobar, Francisco; Freixas Bosch, Josep; Puente del Campo, María AlbinanoBinary voting systems, usually represented by simple games, constitute a main DSS topic. A crucial feature of
such a system is the easiness with which a proposal can be collectively accepted, which is measured by the
“decisiveness index” of the corresponding game. We study here several functions related to the decisiveness
of any simple game. The analysis, including the asymptotic behavior as the number n of players increases, is
restricted to decisive symmetric games and their compositions, and it is assumed that all players have a
common probability p to vote for the proposal. We show that, for n large enough, a small variation, either
positive or negative, in p when p=1/2 takes the decisiveness to quickly approach, respectively, 1 or 0.
Moreover, we analyze the speed of the decisiveness convergence.Decisiveness of decisive symmetric games
http://hdl.handle.net/2117/12437
Title: Decisiveness of decisive symmetric games
Authors: Carreras Escobar, Francisco; Freixas Bosch, Josep; Puente del Campo, María Albina
Abstract: Binary voting systems, usually represented by simple games, constitute a main DSS topic. A crucial feature of such a system is the easiness with which a proposal can be collectively accepted, which is measured by the "decisiveness index" of the corresponding game. We study here several functions related to the decisiveness of any simple game. The analysis, including the asymptotic behavior as the number n of players increases, is restricited to decisive symmetric gammes and their compositions, and it is assumed that all players have a common probability p to vote for the proposal. We show that, for n large enough, a small variation, either positive or negaive, in p when p=1/2 takes the decisiveness to quickly approach , respectively, 1 or 0. Moreover, we analyze the speed of the decisiveness convergence.
Description: Reseach supported by Grant SGR 2009-01029 of the Catalonia Government (Generalitat de Catalunya) and Frants MTM 2006-06064 and MTM 2009-08037 of the Science and Innovation Spanish Ministry and the European Regional Development Fund.Fri, 29 Apr 2011 15:46:53 GMThttp://hdl.handle.net/2117/124372011-04-29T15:46:53ZCarreras Escobar, Francisco; Freixas Bosch, Josep; Puente del Campo, María AlbinanoBinary voting systems, usually represented by simple games, constitute a main DSS topic. A crucial feature of such a system is the easiness with which a proposal can be collectively accepted, which is measured by the "decisiveness index" of the corresponding game. We study here several functions related to the decisiveness of any simple game. The analysis, including the asymptotic behavior as the number n of players increases, is restricited to decisive symmetric gammes and their compositions, and it is assumed that all players have a common probability p to vote for the proposal. We show that, for n large enough, a small variation, either positive or negaive, in p when p=1/2 takes the decisiveness to quickly approach , respectively, 1 or 0. Moreover, we analyze the speed of the decisiveness convergence.Symmetric coalitional binomial semivalues
http://hdl.handle.net/2117/12436
Title: Symmetric coalitional binomial semivalues
Authors: Carreras Escobar, Francisco; Puente del Campo, María Albina
Abstract: We introduce here a family of mixed coalitional values. they extend the binomial semivalues to games endowed with a coalition structure, satisfy the property of symmetry in the quotidient game and the quotient game property, generalize the symmetric coalitional Banzhaf value introduced by Alonso and Fiestras and link and merge the shapley value and the binomial semivalues. A computational procedure in terms of the multilinear extension of the original game is also provided and an application to political science is sketched.
Description: Reseach supported by Grant SGR 2009-01029 of the Catalonia Government (Generalitat de Catalunya) and Frants MTM 2006-06064 and MTM 2009-08037 of the Science and Innovation Spanish Ministry and the European Regional Development Fund.Fri, 29 Apr 2011 15:19:06 GMThttp://hdl.handle.net/2117/124362011-04-29T15:19:06ZCarreras Escobar, Francisco; Puente del Campo, María AlbinanoWe introduce here a family of mixed coalitional values. they extend the binomial semivalues to games endowed with a coalition structure, satisfy the property of symmetry in the quotidient game and the quotient game property, generalize the symmetric coalitional Banzhaf value introduced by Alonso and Fiestras and link and merge the shapley value and the binomial semivalues. A computational procedure in terms of the multilinear extension of the original game is also provided and an application to political science is sketched.The proportional coalitional Shapley value
http://hdl.handle.net/2117/12035
Title: The proportional coalitional Shapley value
Authors: Alonso Meijide, José María; Carreras Escobar, Francisco
Abstract: We propose a modification of the Shapley value for monotonic games with a coalition structure. The resulting coalitional value is a twofold extension of the Shapley value in the following sense: (1) the amount obtained by any union coincides with the Shapley value of the union in the quotient game; and (2) the players of the union share this amount proportionally to their Shapley value in the original game (i.e., without unions). We provide axiomatic characterizations of this value close to those existing in the literature for the Owen value and include applications to coalition formation in bankruptcy and voting problems.Wed, 23 Mar 2011 15:15:00 GMThttp://hdl.handle.net/2117/120352011-03-23T15:15:00ZAlonso Meijide, José María; Carreras Escobar, FrancisconoWe propose a modification of the Shapley value for monotonic games with a coalition structure. The resulting coalitional value is a twofold extension of the Shapley value in the following sense: (1) the amount obtained by any union coincides with the Shapley value of the union in the quotient game; and (2) the players of the union share this amount proportionally to their Shapley value in the original game (i.e., without unions). We provide axiomatic characterizations of this value close to those existing in the literature for the Owen value and include applications to coalition formation in bankruptcy and voting problems.Power and potential maps induced by any semivalue: some algebraic properties and computation by multilinear extensions
http://hdl.handle.net/2117/12033
Title: Power and potential maps induced by any semivalue: some algebraic properties and computation by multilinear extensions
Authors: Carreras Escobar, Francisco; Giménez Pradales, José Miguel
Abstract: The notions of total power and potential, both defined for any semivalue, give rise to two endomorphisms of the vector space of cooperative games on any given player set where the semivalue is defined. Several properties of these linear mappings are stated and the role of unanimity games as eigenvectors is described. We also relate in both cases the multilinear extension of the image game to the multilinear extension of the original game. As a consequence, we derive a method to compute for any semivalue by means of multilinear extensions, in the original game and also in all its subgames, (a) the total power, (b) the potential, and (c) the allocation to each player given by the semivalue.Wed, 23 Mar 2011 14:47:37 GMThttp://hdl.handle.net/2117/120332011-03-23T14:47:37ZCarreras Escobar, Francisco; Giménez Pradales, José MiguelnoThe notions of total power and potential, both defined for any semivalue, give rise to two endomorphisms of the vector space of cooperative games on any given player set where the semivalue is defined. Several properties of these linear mappings are stated and the role of unanimity games as eigenvectors is described. We also relate in both cases the multilinear extension of the image game to the multilinear extension of the original game. As a consequence, we derive a method to compute for any semivalue by means of multilinear extensions, in the original game and also in all its subgames, (a) the total power, (b) the potential, and (c) the allocation to each player given by the semivalue.Detection of paradoxes of power indices for simple games
http://hdl.handle.net/2117/11723
Title: Detection of paradoxes of power indices for simple games
Authors: Freixas Bosch, Josep; Molinero Albareda, XavierTue, 08 Mar 2011 16:06:51 GMThttp://hdl.handle.net/2117/117232011-03-08T16:06:51ZFreixas Bosch, Josep; Molinero Albareda, Xavierno