GRTJ - Grup de Recerca en Teoria de Jocs
http://hdl.handle.net/2117/3429
2016-10-22T17:02:52ZPure 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
2016-09-08T11:00:25ZCarreras 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.
2016-07-28T11:25:42ZLiu, 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.
2016-07-21T11:26:45ZFreixas 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.Some properties for probabilistic and multinomial (probabilistic) values on cooperative games
http://hdl.handle.net/2117/89025
Some properties for probabilistic and multinomial (probabilistic) values on cooperative games
Domènech Blázquez, Margarita; Giménez Pradales, José Miguel; Puente del Campo, María Albina
We investigate the conditions for the coefficients of probabilistic and multinomial values of cooperative games necessary and/or sufficient in order to satisfy some properties, including marginal contributions, balanced contributions, desirability relation and null player exclusion property. Moreover, a similar analysis is conducted for transfer property of probabilistic power indices on the domain of simple games.
This is an Accepted Manuscript of an article published by Taylor & Francis in Optimization on 18-02-2016, available online: http://www.tandfonline.com/10.1080/02331934.2016.1147035.
2016-07-21T10:15:08ZDomènech Blázquez, MargaritaGiménez Pradales, José MiguelPuente del Campo, María AlbinaWe investigate the conditions for the coefficients of probabilistic and multinomial values of cooperative games necessary and/or sufficient in order to satisfy some properties, including marginal contributions, balanced contributions, desirability relation and null player exclusion property. Moreover, a similar analysis is conducted for transfer property of probabilistic power indices on the domain of simple games.Some advances in the theory of voting systems based on experimental algorithms
http://hdl.handle.net/2117/87345
Some advances in the theory of voting systems based on experimental algorithms
Freixas Bosch, Josep; Molinero Albareda, Xavier
In voting systems, game theory, switching functions, threshold logic, hypergraphs or coherent structures there is an important problem that consists in determining the weightedness of a voting system by means of trades among voters in sets of coalitions. The fundamental theorem by Taylor and Zwicker cite{TaZw92} establishes the equivalence between weighted voting games and $k$-trade robust games for each positive integer $k$. Moreover, they also construct, in cite{TaZw95}, a succession of games $G_k$ based on magic squares which are $(k-1)$-trade robust but not $k$-trade robust, each one of these games $G_k$ has $k^2$ players. The goal of this paper is to provide improvements by means of different experiments to the problem described above. In particular, we will classify all complete games (a basic class of games) of less than eight players according to they are: a weighted voting game or a game which is $(k-1)$-trade robust but not $k$-trade robust for all values of $k$. As a consequence it will we showed the existence of games with less than $k^2$ players which are $(k-1)$-trade robust but not $k$-trade robust. We want to point out that the classifications obtained in this paper by means of experiments are new in the mentioned fields.
2016-05-26T08:32:43ZFreixas Bosch, JosepMolinero Albareda, XavierIn voting systems, game theory, switching functions, threshold logic, hypergraphs or coherent structures there is an important problem that consists in determining the weightedness of a voting system by means of trades among voters in sets of coalitions. The fundamental theorem by Taylor and Zwicker cite{TaZw92} establishes the equivalence between weighted voting games and $k$-trade robust games for each positive integer $k$. Moreover, they also construct, in cite{TaZw95}, a succession of games $G_k$ based on magic squares which are $(k-1)$-trade robust but not $k$-trade robust, each one of these games $G_k$ has $k^2$ players. The goal of this paper is to provide improvements by means of different experiments to the problem described above. In particular, we will classify all complete games (a basic class of games) of less than eight players according to they are: a weighted voting game or a game which is $(k-1)$-trade robust but not $k$-trade robust for all values of $k$. As a consequence it will we showed the existence of games with less than $k^2$ players which are $(k-1)$-trade robust but not $k$-trade robust. We want to point out that the classifications obtained in this paper by means of experiments are new in the mentioned fields.The cost of getting local monotonicity
http://hdl.handle.net/2117/86881
The cost of getting local monotonicity
Freixas Bosch, Josep; Kurz, Sascha
Committees with yes-no-decisions are commonly modeled as simple games and the ability of a member to influence the group decision is measured by so-called power indices. For a weighted game we say that a power index satisfies local monotonicity if a player who controls a large share of the total weight vote does not have less power than a player with a smaller voting weight. In (Holler, 1982) Manfred Holler introduced the Public Good index. In its unnormalized version, i.e., the raw measure, it counts the number of times that a player belongs to a minimal winning coalition. Unlike the Banzhaf index, it does not count the remaining winning coalitions in which the player is crucial. Holler noticed that his index does not satisfy local monotonicity, a fact that can be seen either as a major drawback (Felsenthal & Machover, 1998, 221 ff.)or as an advantage (Holler & Napel 2004). In this paper we consider a convex combination of the two indices and require the validity of local monotonicity. We prove that the cost of obtaining it is high, i.e., the achievable new indices satisfying local monotonicity are closer to the Banzhaf index than to the Public Good index. All these achievable new indices are more solidary than the Banzhaf index, which makes them as very suitable candidates to divide a public good. As a generalization we consider convex combinations of either: the Shift index, the Public Good index, and the Banzhaf index, or alternatively: the Shift Deegan-Packel, Deegan-Packel, and Johnston indices.
2016-05-10T14:22:58ZFreixas Bosch, JosepKurz, SaschaCommittees with yes-no-decisions are commonly modeled as simple games and the ability of a member to influence the group decision is measured by so-called power indices. For a weighted game we say that a power index satisfies local monotonicity if a player who controls a large share of the total weight vote does not have less power than a player with a smaller voting weight. In (Holler, 1982) Manfred Holler introduced the Public Good index. In its unnormalized version, i.e., the raw measure, it counts the number of times that a player belongs to a minimal winning coalition. Unlike the Banzhaf index, it does not count the remaining winning coalitions in which the player is crucial. Holler noticed that his index does not satisfy local monotonicity, a fact that can be seen either as a major drawback (Felsenthal & Machover, 1998, 221 ff.)or as an advantage (Holler & Napel 2004). In this paper we consider a convex combination of the two indices and require the validity of local monotonicity. We prove that the cost of obtaining it is high, i.e., the achievable new indices satisfying local monotonicity are closer to the Banzhaf index than to the Public Good index. All these achievable new indices are more solidary than the Banzhaf index, which makes them as very suitable candidates to divide a public good. As a generalization we consider convex combinations of either: the Shift index, the Public Good index, and the Banzhaf index, or alternatively: the Shift Deegan-Packel, Deegan-Packel, and Johnston indices.Minimal 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.
2016-04-27T07:22:54ZFreixas 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.
2016-04-21T13:57:53ZMolinero 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.
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.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
2016-03-10T15:58:37ZFreixas 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.