GRTJ - Grup de Recerca en Teoria de Jocs
http://hdl.handle.net/2117/3429
2017-09-21T19:05:16ZCombinatorial structures to modeling simple games and applications
http://hdl.handle.net/2117/107881
Combinatorial 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.On the characterization of weighted simple games
http://hdl.handle.net/2117/107644
On the characterization of weighted simple games
Freixas Bosch, Josep; Freixas Boleda, Marc; Kurz, Sascha
This paper has a twofold scope. The first one is to clarify and put in evidence the isomorphic character of two theories developed in quite different fields: on one side, threshold logic, on the other side, simple games. One of the main purposes in both theories is to determine when a simple game is representable as a weighted game, which allows a very compact and easily comprehensible representation. Deep results were found in threshold logic in the sixties and seventies for this problem. However, game theory has taken the lead and some new results have been obtained for the problem in the past two decades. The second and main goal of this paper is to provide some new results on this problem and propose several open questions and conjectures for future research. The results we obtain depend on two significant parameters of the game: the number of types of equivalent players and the number of types of shift-minimal winning coalitions.
2017-09-14T17:51:00ZFreixas Bosch, JosepFreixas Boleda, MarcKurz, SaschaThis paper has a twofold scope. The first one is to clarify and put in evidence the isomorphic character of two theories developed in quite different fields: on one side, threshold logic, on the other side, simple games. One of the main purposes in both theories is to determine when a simple game is representable as a weighted game, which allows a very compact and easily comprehensible representation. Deep results were found in threshold logic in the sixties and seventies for this problem. However, game theory has taken the lead and some new results have been obtained for the problem in the past two decades. The second and main goal of this paper is to provide some new results on this problem and propose several open questions and conjectures for future research. The results we obtain depend on two significant parameters of the game: the number of types of equivalent players and the number of types of shift-minimal winning coalitions.Separability by semivalues modified for games with coalition structure
http://hdl.handle.net/2117/105390
Separability by semivalues modified for games with coalition structure
Amer Ramon, Rafael; Giménez Pradales, José Miguel
Two games are inseparable by semivalues if both games obtain the same allocation whatever semivalue is considered. The problem of separability by semivalues reduces to separability from the null game. For four or more players, the vector subspace of games inseparable from the null game by semivalues contains games different to zero-game. Now, for five or more players, the consideration of a priori coalition blocks in the player set allows us to reduce in a significant way the dimension of the vector subspace of games inseparable from the null game. For these subspaces we provide basis formed by games of a particular type.
The original publication is available at www.rairo-ro.org
2017-06-13T15:21:57ZAmer Ramon, RafaelGiménez Pradales, José MiguelTwo games are inseparable by semivalues if both games obtain the same allocation whatever semivalue is considered. The problem of separability by semivalues reduces to separability from the null game. For four or more players, the vector subspace of games inseparable from the null game by semivalues contains games different to zero-game. Now, for five or more players, the consideration of a priori coalition blocks in the player set allows us to reduce in a significant way the dimension of the vector subspace of games inseparable from the null game. For these subspaces we provide basis formed by games of a particular type.Using the multilinear extension to study some probabilistic power indices
http://hdl.handle.net/2117/104580
Using the multilinear extension to study some probabilistic power indices
Freixas Bosch, Josep; Pons Vallès, Montserrat
We consider binary voting systems modeled by a simple game, in which voters vote independently of each other, and the probability distribution over coalitions is known. The Owen’s multilinear extension of the simple game is used to improve the use and the computation of three indices defined in this model: the decisiveness index, which is an extension of the Banzhaf index, the success index, which is an extension of the Rae index, and the luckiness index. This approach leads us to prove new properties and inter-relations between these indices. In particular it is proved that the ordinal equivalence between success and decisiveness indices is achieved in any game if and only if the probability distribution is anonymous. In the anonymous case, the egalitarianism of the three indices is compared, and it is also proved that, for these distributions, decisiveness and success indices respect the strength of the seats, whereas luckiness reverses this order.
The final publication is available at Springer via http://dx.doi.org/10.1007/s10726-016-9514-6
2017-05-17T14:32:45ZFreixas Bosch, JosepPons Vallès, MontserratWe consider binary voting systems modeled by a simple game, in which voters vote independently of each other, and the probability distribution over coalitions is known. The Owen’s multilinear extension of the simple game is used to improve the use and the computation of three indices defined in this model: the decisiveness index, which is an extension of the Banzhaf index, the success index, which is an extension of the Rae index, and the luckiness index. This approach leads us to prove new properties and inter-relations between these indices. In particular it is proved that the ordinal equivalence between success and decisiveness indices is achieved in any game if and only if the probability distribution is anonymous. In the anonymous case, the egalitarianism of the three indices is compared, and it is also proved that, for these distributions, decisiveness and success indices respect the strength of the seats, whereas luckiness reverses this order.On alpha-roughly weighted games
http://hdl.handle.net/2117/103235
On alpha-roughly weighted games
Freixas Bosch, Josep; Kurz, Sascha
Very recently Gvozdeva, Hemaspaandra, and Slinko (2011) h
ave introduced three hierarchies for simple games in order to measure the distance of a given simple game to the class of weighted voting games or roughly weighted voting games. Their third class C aconsists of all simple games
permitting a weighted representation such that each winnin
g coalition has a weight of at least 1 and each losing coalition a weight of at most a. We continue their work and contribute some new results on the possible values of a for a given number of voters.
2017-04-03T15:53:36ZFreixas Bosch, JosepKurz, SaschaVery recently Gvozdeva, Hemaspaandra, and Slinko (2011) h
ave introduced three hierarchies for simple games in order to measure the distance of a given simple game to the class of weighted voting games or roughly weighted voting games. Their third class C aconsists of all simple games
permitting a weighted representation such that each winnin
g coalition has a weight of at least 1 and each losing coalition a weight of at most a. We continue their work and contribute some new results on the possible values of a for a given number of voters.The complexity of testing properties of simple games
http://hdl.handle.net/2117/103171
The complexity of testing properties of simple games
Freixas Bosch, Josep; Molinero Albareda, Xavier; Olsen, Martin; Serna Iglesias, María José
Simple games cover voting systems in which a single alternative, such as a bill or an amendment, is pitted against the status quo. A simple game or a yes-no voting system is a set of rules that specifies exactly which collections of ``yea'' votes yield passage of the issue at hand. A collection of ``yea'' voters forms a winning coalition.
We are interested on performing a complexity analysis of problems on such games depending on the game representation. We consider four natural explicit representations, winning, loosing, minimal winning, and maximal loosing. We first analyze the computational complexity of obtaining a particular representation of a simple game from a different one. We show that some cases this transformation can be done in polynomial time while the others require exponential time. The second question is classifying the complexity for testing whether a game is simple or weighted. We show that for the four types of representation both problem can be solved in polynomial time. Finally, we provide results on the complexity of testing whether a simple game or a weighted game is of a special type. In this way, we analyze strongness, properness, decisiveness and homogeneity, which are desirable properties to be fulfilled for a simple game.
2017-03-31T15:48:07ZFreixas Bosch, JosepMolinero Albareda, XavierOlsen, MartinSerna Iglesias, María JoséSimple games cover voting systems in which a single alternative, such as a bill or an amendment, is pitted against the status quo. A simple game or a yes-no voting system is a set of rules that specifies exactly which collections of ``yea'' votes yield passage of the issue at hand. A collection of ``yea'' voters forms a winning coalition.
We are interested on performing a complexity analysis of problems on such games depending on the game representation. We consider four natural explicit representations, winning, loosing, minimal winning, and maximal loosing. We first analyze the computational complexity of obtaining a particular representation of a simple game from a different one. We show that some cases this transformation can be done in polynomial time while the others require exponential time. The second question is classifying the complexity for testing whether a game is simple or weighted. We show that for the four types of representation both problem can be solved in polynomial time. Finally, we provide results on the complexity of testing whether a simple game or a weighted game is of a special type. In this way, we analyze strongness, properness, decisiveness and homogeneity, which are desirable properties to be fulfilled for a simple game.Weighted voting, abstention and multiple levels of approval
http://hdl.handle.net/2117/103170
Weighted voting, abstention and multiple levels of approval
Freixas Bosch, Josep; Zwicker, William S.
In this paper we introduce the class of simple games with several ordered levels of approval in the input and in the output – the ( j,k) simple games – and propose a definition for weighted games in this context. Abstention is treated as a level of input approval intermediate to votes of yes and no. Our main theorem provides a combinatorial characterization, in terms of what we call grade trade robustness, of weighted ( j,k) games within the class of all ( j,k) simple games. We also introduce other subclasses of ( j,k) simple games and classify several examples. For example, we show the existence of a weighted representation for the UNSC, seen as a voting system in which abstention is permitted.
Research partially supported by Grant 1999BEAI400096 of the Commissioner for Universities and Research of the Catalonia Generalitat and by Grant BFM 2000–0968 of the Spanish Ministry of Science and Technology. The authors would like to thank Larry Becker, Clifford Brown, Vin Moscardelli, and Fred Jonas for their assistance. Extensive remarks by Moshé Machover as well as comments by an anonymous referee greatly improved the manuscript.
The final publication is available at Springer via http://dx.doi.org/10.1007/s00355-003-0212-3.
2017-03-31T15:30:18ZFreixas Bosch, JosepZwicker, William S.In this paper we introduce the class of simple games with several ordered levels of approval in the input and in the output – the ( j,k) simple games – and propose a definition for weighted games in this context. Abstention is treated as a level of input approval intermediate to votes of yes and no. Our main theorem provides a combinatorial characterization, in terms of what we call grade trade robustness, of weighted ( j,k) games within the class of all ( j,k) simple games. We also introduce other subclasses of ( j,k) simple games and classify several examples. For example, we show the existence of a weighted representation for the UNSC, seen as a voting system in which abstention is permitted.
Research partially supported by Grant 1999BEAI400096 of the Commissioner for Universities and Research of the Catalonia Generalitat and by Grant BFM 2000–0968 of the Spanish Ministry of Science and Technology. The authors would like to thank Larry Becker, Clifford Brown, Vin Moscardelli, and Fred Jonas for their assistance. Extensive remarks by Moshé Machover as well as comments by an anonymous referee greatly improved the manuscript.Ability to separate situations with a priori coalition structures by means of symmetric solutions
http://hdl.handle.net/2117/102517
Ability 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.Effect of a science communication event on students’ attitudes towards science and technology
http://hdl.handle.net/2117/102416
Effect of a science communication event on students’ attitudes towards science and technology
Torras Melenchón, Núria; Grau Vilalta, Maria Dolors; Font Soldevila, Josep; Freixas Bosch, Josep
2017-03-14T08:15:19ZTorras Melenchón, NúriaGrau Vilalta, Maria DolorsFont Soldevila, JosepFreixas Bosch, JosepA new procedure to calculate the Owen value
http://hdl.handle.net/2117/102250
A 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.