GRTJ  Grup de Recerca en Teoria de Jocs
http://hdl.handle.net/2117/3429
20210725T17:24:16Z

Influence decision models: from cooperative game theory to social network analysis
http://hdl.handle.net/2117/350018
Influence decision models: from cooperative game theory to social network analysis
Molinero Albareda, Xavier; Riquelme Csori, Fabián
Cooperative game theory considers simple games and influence games as essential classes of games. A simple game can be viewed as a model of voting systems in which a single alternative, such as a bill or an amendment, is pitted against the status quo. An influence game is a cooperative game in which a team of players (or coalition) succeeds if it is able to convince sufficiently many agents to participate in a task. Furthermore, influence decision models allow to represent discrete system dynamics as graphs whose nodes are activated according to an influence spread model. It let us to depth in the social network analysis. All these concepts are applied to a wide variety of disciplines, such as social sciences, economics, marketing, cognitive sciences, political science, biology, computer science, among others. In this survey we present different advances in these topics, joint work with M. Serna.
These advances include representations of simple games, the definition of influence games, and how to characterize different problems on influence games (measures, values, properties and problems for particular cases with respect to both the spread of influence and the structure of the graph). Moreover, we also present equivalent models to the simple games, the computation of satisfaction and power in collective decisionmaking models, and the definition of new centrality measures used for social network analysis. In addition, several interesting computational complexity results have been found.
20210723T11:03:55Z
Molinero Albareda, Xavier
Riquelme Csori, Fabián
Cooperative game theory considers simple games and influence games as essential classes of games. A simple game can be viewed as a model of voting systems in which a single alternative, such as a bill or an amendment, is pitted against the status quo. An influence game is a cooperative game in which a team of players (or coalition) succeeds if it is able to convince sufficiently many agents to participate in a task. Furthermore, influence decision models allow to represent discrete system dynamics as graphs whose nodes are activated according to an influence spread model. It let us to depth in the social network analysis. All these concepts are applied to a wide variety of disciplines, such as social sciences, economics, marketing, cognitive sciences, political science, biology, computer science, among others. In this survey we present different advances in these topics, joint work with M. Serna.
These advances include representations of simple games, the definition of influence games, and how to characterize different problems on influence games (measures, values, properties and problems for particular cases with respect to both the spread of influence and the structure of the graph). Moreover, we also present equivalent models to the simple games, the computation of satisfaction and power in collective decisionmaking models, and the definition of new centrality measures used for social network analysis. In addition, several interesting computational complexity results have been found.

Decay of quasistatic porousthermoelastic waves
http://hdl.handle.net/2117/348163
Decay of quasistatic porousthermoelastic waves
Magaña Nieto, Antonio; Quintanilla de Latorre, Ramón
We study the behavior in time of the solutions to several systems of equations for porousthermoelastic problems when one of the variables is considered to be quasistatic or, in other words, whose second time derivative can be neglected. We analyze three different situations using the classical Fourier law and also the type II or type III Green–Naghdi heat conduction models
20210630T11:27:06Z
Magaña Nieto, Antonio
Quintanilla de Latorre, Ramón
We study the behavior in time of the solutions to several systems of equations for porousthermoelastic problems when one of the variables is considered to be quasistatic or, in other words, whose second time derivative can be neglected. We analyze three different situations using the classical Fourier law and also the type II or type III Green–Naghdi heat conduction models

On the enumeration of bipartite simple games
http://hdl.handle.net/2117/346977
On the enumeration of bipartite simple games
Freixas Bosch, Josep; Samaniego Vidal, Daniel
This paper provides a classification of all monotonic bipartite simple games. The problem we deal with is very versatile since simple games are inequivalent monotonic Boolean functions, functions that are used in many fields such as game theory, neural networks, artificial intelligence, reliability or multiplecriteria decisionmaking. The obtained classification can be implemented in an algorithm able to enumerate bipartite simple games. These numbers provide some light on enumerations of several subclasses of bipartite simple games, for which we find formulas.
Complete simple games, a subclass of all simple games for which the desirability relation is a complete preordering, were already classified by means of two parameters: a vector and a matrix fulfilling some conditions. Complete simple games are inequivalent monotonic regular Boolean functions. In this paper, we deduce a procedure for bipartite noncomplete games, which allows enumerating the number of bipartite simple games. Several formulas are obtained, in particular polynomial expressions for the number of bicameral meet games and the number of bicameral join games, two types of voting systems widely used in practice.
© 2021. This manuscript version is made available under the CCBYNCND 4.0 license http://creativecommons.org/licenses/byncnd/4.0/
20210609T14:13:10Z
Freixas Bosch, Josep
Samaniego Vidal, Daniel
This paper provides a classification of all monotonic bipartite simple games. The problem we deal with is very versatile since simple games are inequivalent monotonic Boolean functions, functions that are used in many fields such as game theory, neural networks, artificial intelligence, reliability or multiplecriteria decisionmaking. The obtained classification can be implemented in an algorithm able to enumerate bipartite simple games. These numbers provide some light on enumerations of several subclasses of bipartite simple games, for which we find formulas.
Complete simple games, a subclass of all simple games for which the desirability relation is a complete preordering, were already classified by means of two parameters: a vector and a matrix fulfilling some conditions. Complete simple games are inequivalent monotonic regular Boolean functions. In this paper, we deduce a procedure for bipartite noncomplete games, which allows enumerating the number of bipartite simple games. Several formulas are obtained, in particular polynomial expressions for the number of bicameral meet games and the number of bicameral join games, two types of voting systems widely used in practice.

An extension and an alternative characterization of May’s theorem
http://hdl.handle.net/2117/345904
An extension and an alternative characterization of May’s theorem
Freixas Bosch, Josep; Pons Vallès, Montserrat
The context of this work is a voting scenario in which each voter expresses his/her level of affinity about a proposal, by choosing a value in the set J={j,…,1,0,1,…,j}, and these individual votes produce a collective result, in the same set J, through a decision function. The simple majority, defined for j=1, is a widely used example of such a decision function. In this paper, a set of independent axioms is proved to uniquely characterize the jmajority decision function. The jmajority decision is defined for any positive integer j, and it coincides with the simple majority decision when j=1. In this way, this axiomatic characterization meets two goals: it gives a new characterization of the simple majority decision when j=1 and it extends May’s theorem to this broader context.
This is a postpeerreview, precopyedit version of an article published in Annals of Operations Research. The final authenticated version is available online at: http://dx.doi.org/10.1007/s1047902104044w.
20210519T11:21:42Z
Freixas Bosch, Josep
Pons Vallès, Montserrat
The context of this work is a voting scenario in which each voter expresses his/her level of affinity about a proposal, by choosing a value in the set J={j,…,1,0,1,…,j}, and these individual votes produce a collective result, in the same set J, through a decision function. The simple majority, defined for j=1, is a widely used example of such a decision function. In this paper, a set of independent axioms is proved to uniquely characterize the jmajority decision function. The jmajority decision is defined for any positive integer j, and it coincides with the simple majority decision when j=1. In this way, this axiomatic characterization meets two goals: it gives a new characterization of the simple majority decision when j=1 and it extends May’s theorem to this broader context.

An appropriate way to extend the Banzhaf index for multiple levels of approval
http://hdl.handle.net/2117/341788
An appropriate way to extend the Banzhaf index for multiple levels of approval
Freixas Bosch, Josep; Pons Vallès, Montserrat
The Banzhaf power index for games admits several extensions if the players have more than two ordered voting options. In this paper we prove that the most intuitive and recognized extension of the index fails to preserve the desirability relation for games with more than three ordered input levels of approval, a failure that undermines the index to be a good measure of power. This leads us to think of an alternative to the Banzhaf index for several input levels of approval. We propose a candidate for which it is proved that: (1) coincides with the Banzhaf index for simple games, (2) it is proportional to its known extension for three levels of approval, and (3) preserves the desirability relation regardless of the number of input levels of approval. This new index is based on measuring the total capacity the player has to alter the outcome. In addition, it can be expressed through a very appropriate mathematical formulation that greatly facilitates its computation. Defining extensions of wellestablished notions in a wider context requires a careful analysis. Different extensions can provide complementary nuances and, when this occurs, none of them can be considered to be ‘the’ extension. As shown in this paper, this situation applies when trying to extend the Banzhaf power index from simple games to the broader context of games with several ordered input levels of approval.
This is a postpeerreview, precopyedit version of an article published in Group decision and negotiation. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10726020097187.
20210316T12:37:57Z
Freixas Bosch, Josep
Pons Vallès, Montserrat
The Banzhaf power index for games admits several extensions if the players have more than two ordered voting options. In this paper we prove that the most intuitive and recognized extension of the index fails to preserve the desirability relation for games with more than three ordered input levels of approval, a failure that undermines the index to be a good measure of power. This leads us to think of an alternative to the Banzhaf index for several input levels of approval. We propose a candidate for which it is proved that: (1) coincides with the Banzhaf index for simple games, (2) it is proportional to its known extension for three levels of approval, and (3) preserves the desirability relation regardless of the number of input levels of approval. This new index is based on measuring the total capacity the player has to alter the outcome. In addition, it can be expressed through a very appropriate mathematical formulation that greatly facilitates its computation. Defining extensions of wellestablished notions in a wider context requires a careful analysis. Different extensions can provide complementary nuances and, when this occurs, none of them can be considered to be ‘the’ extension. As shown in this paper, this situation applies when trying to extend the Banzhaf power index from simple games to the broader context of games with several ordered input levels of approval.

On the enumeration of Boolean functions with distinguished variables
http://hdl.handle.net/2117/341224
On the enumeration of Boolean functions with distinguished variables
Freixas Bosch, Josep
Boolean functions have a fundamental role in neural networks and machine learning. Enumerating these functions and significant subclasses is a highly complex problem. Therefore, it is of interest to study subclasses that escape this limitation and can be enumerated by means of sequences depending on the number of variables. In this article, we obtain seven new formulas corresponding to enumerations of some subclasses of Boolean functions. The versatility of these functions does the problem interesting to several different fields as game theory, hypergraphs, reliability, cryptography or logic gates.
This is a postpeerreview, precopyedit version of an article published in Soft computing. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00500020054225
20210309T09:37:32Z
Freixas Bosch, Josep
Boolean functions have a fundamental role in neural networks and machine learning. Enumerating these functions and significant subclasses is a highly complex problem. Therefore, it is of interest to study subclasses that escape this limitation and can be enumerated by means of sequences depending on the number of variables. In this article, we obtain seven new formulas corresponding to enumerations of some subclasses of Boolean functions. The versatility of these functions does the problem interesting to several different fields as game theory, hypergraphs, reliability, cryptography or logic gates.

A characterization of weighted simple games based on pseudoweightings
http://hdl.handle.net/2117/337122
A characterization of weighted simple games based on pseudoweightings
Freixas Bosch, Josep
The paper provides a new characterization of weighted games within the class of simple games. It is based on a stronger form of the pointsetadditive pseudoweighting property of simple games. The characterization obtained is of interest in various research fields such as game theory, coherent structures, logic gates, operations research and Boolean algebra. A (monotonic) simple game corresponds to an inequivalent (monotonic) function in Boolean algebra and a weighted game corresponds to a threshold function. The characterization obtained provides a better understanding of these mathematical structures while opening new prospects for solving numerous open problems in these areas.
This is a postpeerreview, precopyedit version of an article published in Optimization letters. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11590020016473
20210209T09:55:36Z
Freixas Bosch, Josep
The paper provides a new characterization of weighted games within the class of simple games. It is based on a stronger form of the pointsetadditive pseudoweighting property of simple games. The characterization obtained is of interest in various research fields such as game theory, coherent structures, logic gates, operations research and Boolean algebra. A (monotonic) simple game corresponds to an inequivalent (monotonic) function in Boolean algebra and a weighted game corresponds to a threshold function. The characterization obtained provides a better understanding of these mathematical structures while opening new prospects for solving numerous open problems in these areas.

Exponential decay of solutions in type II porousthermoelasticity with quasistatic microvoids
http://hdl.handle.net/2117/328352
Exponential decay of solutions in type II porousthermoelasticity with quasistatic microvoids
Magaña Nieto, Antonio; Miranville, Alain; Quintanilla de Latorre, Ramón
In this note we study the problem proposed by the onedimensional thermoporouselasticity of type II with quasistatic microvoids or, in mathematical terms, when the second time derivative of the volume fraction is so small that it can be negligible. It is known that the isothermal deformations decay in a slow way. Here we prove that the introduction of a conservative mechanism, as it is the type II heat conduction, makes the deformations damp generically in an exponential way, which is a striking fact.
20200903T11:21:42Z
Magaña Nieto, Antonio
Miranville, Alain
Quintanilla de Latorre, Ramón
In this note we study the problem proposed by the onedimensional thermoporouselasticity of type II with quasistatic microvoids or, in mathematical terms, when the second time derivative of the volume fraction is so small that it can be negligible. It is known that the isothermal deformations decay in a slow way. Here we prove that the introduction of a conservative mechanism, as it is the type II heat conduction, makes the deformations damp generically in an exponential way, which is a striking fact.

A porothermoelastic problem with dissipative heat conduction
http://hdl.handle.net/2117/328295
A porothermoelastic problem with dissipative heat conduction
Bazarra, Noelia; Fernández, Jose R.; Magaña Nieto, Antonio; Quintanilla de Latorre, Ramón
In this work, we study from the mathematical and numerical points of view a porothermoelastic problem. A longterm memory is assumed on the heat equation. Under some assumptions on the constitutive tensors, the resulting linear system is composed of hyperbolic partial differential equations with a dissipative mechanism in the temperature equation. An existence and uniqueness result is proved using the theory of contractive semigroups.
Then, a fully discrete approximation is introduced applying the finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives. A discrete stability property is obtained. A priori error estimates are also shown, from which the linear convergence of the approximation is derived under suitable additional regularity conditions. Finally, one and twonumerical simulations are presented to demonstrate the accuracy of the algorithm and the behavior of the solution.
20200902T11:32:04Z
Bazarra, Noelia
Fernández, Jose R.
Magaña Nieto, Antonio
Quintanilla de Latorre, Ramón
In this work, we study from the mathematical and numerical points of view a porothermoelastic problem. A longterm memory is assumed on the heat equation. Under some assumptions on the constitutive tensors, the resulting linear system is composed of hyperbolic partial differential equations with a dissipative mechanism in the temperature equation. An existence and uniqueness result is proved using the theory of contractive semigroups.
Then, a fully discrete approximation is introduced applying the finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives. A discrete stability property is obtained. A priori error estimates are also shown, from which the linear convergence of the approximation is derived under suitable additional regularity conditions. Finally, one and twonumerical simulations are presented to demonstrate the accuracy of the algorithm and the behavior of the solution.

Exponential decay in onedimensional Type II/III thermoelasticity with two porosities
http://hdl.handle.net/2117/187178
Exponential decay in onedimensional Type II/III thermoelasticity with two porosities
Magaña Nieto, Antonio; Quintanilla de Latorre, Ramón
In this paper we consider the theory of thermoelasticity with a double porosity structure in the context of the GreenNaghdi types II and III heat conduction models. For the type II, the problem is given by four hyperbolic equations and it is conservative (there is no energy dissipation). We introduce in the system a couple of dissipation mechanisms in order to obtain the exponential de cay of the solutions. To be precise, we introduce a pair of the following damping mechanisms: viscoelasticity, viscoporosities and thermal dissipation. We prove that the system is exponentially stable in three different scenarios: viscoporosity in one structure jointly with thermal dissipation, viscoporosity in each structure, and viscoporosity in one structure jointly with viscoelasticity. However, if viscoelasticity and thermal dissipation are considered together, undamped solutions can be obtained.
20200512T07:21:27Z
Magaña Nieto, Antonio
Quintanilla de Latorre, Ramón
In this paper we consider the theory of thermoelasticity with a double porosity structure in the context of the GreenNaghdi types II and III heat conduction models. For the type II, the problem is given by four hyperbolic equations and it is conservative (there is no energy dissipation). We introduce in the system a couple of dissipation mechanisms in order to obtain the exponential de cay of the solutions. To be precise, we introduce a pair of the following damping mechanisms: viscoelasticity, viscoporosities and thermal dissipation. We prove that the system is exponentially stable in three different scenarios: viscoporosity in one structure jointly with thermal dissipation, viscoporosity in each structure, and viscoporosity in one structure jointly with viscoelasticity. However, if viscoelasticity and thermal dissipation are considered together, undamped solutions can be obtained.