Capítols de llibre
http://hdl.handle.net/2117/3434
Fri, 24 Jan 2020 11:41:47 GMT2020-01-24T11:41:47ZA value for j-cooperative games: some theoretical aspects and applications
http://hdl.handle.net/2117/175451
A value for j-cooperative games: some theoretical aspects and applications
Freixas Bosch, Josep
A value that has all the ingredients to be a generalization of the Shapley value is proposed for a large class of games called j-cooperative games which are closely related to multi-choice games. When it is restricted to cooperative games, i.e. when j equals 2, it coincides with the Shapley value. An explicit formula in terms of some marginal contributions of the characteristic function is provided for the proposed value. Different arguments support it: (1) The value can be inferred from a natural probabilistic model. (2) An axiomatic characterization uniquely determines it. (3) The value is consistent in its particularization from j-cooperative games to j-simple games. This chapter also proposes various ways of calculating the value by giving an alternative expression that does not depend on the marginal contributions. This chapter shows how the technique of generating functions can be applied to determine such a value when the game is a weighted j-simple game. The chapter concludes by presenting several applications, among them the computation of the value for a proposed reform of the UNSC voting system.
This is an Accepted Manuscript of a book chapter published by Routledge/CRC Press in Handbook of the Shapley value on December 6, 2019, available online: https://www.crcpress.com/Handbook-of-the-Shapley-Value/Algaba-Fragnelli-Sanchez-Soriano/p/book/9780815374688
Wed, 22 Jan 2020 14:35:39 GMThttp://hdl.handle.net/2117/1754512020-01-22T14:35:39ZFreixas Bosch, JosepA value that has all the ingredients to be a generalization of the Shapley value is proposed for a large class of games called j-cooperative games which are closely related to multi-choice games. When it is restricted to cooperative games, i.e. when j equals 2, it coincides with the Shapley value. An explicit formula in terms of some marginal contributions of the characteristic function is provided for the proposed value. Different arguments support it: (1) The value can be inferred from a natural probabilistic model. (2) An axiomatic characterization uniquely determines it. (3) The value is consistent in its particularization from j-cooperative games to j-simple games. This chapter also proposes various ways of calculating the value by giving an alternative expression that does not depend on the marginal contributions. This chapter shows how the technique of generating functions can be applied to determine such a value when the game is a weighted j-simple game. The chapter concludes by presenting several applications, among them the computation of the value for a proposed reform of the UNSC voting system.A probabilistic unified approach for power indices in simple games
http://hdl.handle.net/2117/175449
A probabilistic unified approach for power indices in simple games
Freixas Bosch, Josep; Pons Vallès, Montserrat
Many power indices on simple games have been defined trying to measure, under different points of view, the “a priori” importance of a voter in a collective binary voting scenario. A unified probabilistic way to define some of these power indices is considered in this paper. We show that six well-known power indices are obtained under such a probabilistic approach. Moreover, some new power indices can naturally be obtained in this way.
The final publication is available at Springer via https://doi.org/10.1007/978-3-662-60555-4_11
Wed, 22 Jan 2020 14:17:15 GMThttp://hdl.handle.net/2117/1754492020-01-22T14:17:15ZFreixas Bosch, JosepPons Vallès, MontserratMany power indices on simple games have been defined trying to measure, under different points of view, the “a priori” importance of a voter in a collective binary voting scenario. A unified probabilistic way to define some of these power indices is considered in this paper. We show that six well-known power indices are obtained under such a probabilistic approach. Moreover, some new power indices can naturally be obtained in this way.On the exponential decay of solutions in dual-phase-lag porous thermoelasticity
http://hdl.handle.net/2117/167855
On the exponential decay of solutions in dual-phase-lag porous thermoelasticity
Fernández, José Ramón; Magaña Nieto, Antonio; Quintanilla de Latorre, Ramón
In the last years, a big interest has been developed to understand the time decay of solutions for the porous thermoelasticity with different thermal mechanisms. We here want to consider the problem of the one-dimensional porous thermoelasticity when the heat conduction is given by means of the dual-phase-lag theory. We want to give suitable conditions in order to guarantee that the decay of solutions is controlled by a negative exponential. We also want to provide conditions for the slow decay of the solutions.
Mon, 02 Sep 2019 11:34:22 GMThttp://hdl.handle.net/2117/1678552019-09-02T11:34:22ZFernández, José RamónMagaña Nieto, AntonioQuintanilla de Latorre, RamónIn the last years, a big interest has been developed to understand the time decay of solutions for the porous thermoelasticity with different thermal mechanisms. We here want to consider the problem of the one-dimensional porous thermoelasticity when the heat conduction is given by means of the dual-phase-lag theory. We want to give suitable conditions in order to guarantee that the decay of solutions is controlled by a negative exponential. We also want to provide conditions for the slow decay of the solutions.An equivalent formulation for the Shapley value
http://hdl.handle.net/2117/130642
An equivalent formulation for the Shapley value
Freixas Bosch, Josep
An equivalent explicit formula for the Shapley value is provided, its equivalence with the classical one is proven by double induction. The importance of this new formula, in contrast to the classical one, is its capability of being extended to more general classes of games, in particular to j-cooperative games or multichoice games, in which players choose among different levels of participation in the game.
The final authenticated version is available online at: https://doi.org/10.1007/978-3-662-58464-4_1.
Wed, 20 Mar 2019 09:06:34 GMThttp://hdl.handle.net/2117/1306422019-03-20T09:06:34ZFreixas Bosch, JosepAn equivalent explicit formula for the Shapley value is provided, its equivalence with the classical one is proven by double induction. The importance of this new formula, in contrast to the classical one, is its capability of being extended to more general classes of games, in particular to j-cooperative games or multichoice games, in which players choose among different levels of participation in the game.Preorders in simple games
http://hdl.handle.net/2117/113429
Preorders in simple games
Freixas Bosch, Josep; Pons Vallès, Montserrat
Any power index defines a total preorder in a simple game and, thus, induces a hierarchy among its players. The desirability relation, which is also a preorder, induces the same hierarchy as the Banzhaf and the Shapley indices on linear games, i.e., games in which the desirability relation is total. The desirability relation is a sub–preorder of another preorder, the weak desirability relation, and the class of weakly linear games, i.e., games for which the weak desirability relation is total, is larger than the class of linear games. The weak desirability relation induces the same hierarchy as the Banzhaf and the Shapley indices on weakly linear games. In this paper, we define a chain of preorders between the desirability and the weak desirability preorders. From them we obtain new classes of totally preordered games between linear and weakly linear games.
The final authenticated version is available online at: https://doi.org/10.1007/978-3-319-70647-4_5.
Wed, 31 Jan 2018 10:31:34 GMThttp://hdl.handle.net/2117/1134292018-01-31T10:31:34ZFreixas Bosch, JosepPons Vallès, MontserratAny power index defines a total preorder in a simple game and, thus, induces a hierarchy among its players. The desirability relation, which is also a preorder, induces the same hierarchy as the Banzhaf and the Shapley indices on linear games, i.e., games in which the desirability relation is total. The desirability relation is a sub–preorder of another preorder, the weak desirability relation, and the class of weakly linear games, i.e., games for which the weak desirability relation is total, is larger than the class of linear games. The weak desirability relation induces the same hierarchy as the Banzhaf and the Shapley indices on weakly linear games. In this paper, we define a chain of preorders between the desirability and the weak desirability preorders. From them we obtain new classes of totally preordered games between linear and weakly linear games.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.
The final publication is available at link.springer.com via http://dx.doi.org/10.1007/s11238-017-9606-z
Thu, 14 Sep 2017 17:51:00 GMThttp://hdl.handle.net/2117/1076442017-09-14T17:51:00ZFreixas 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.Pure bargaining problems and the Shapley rule
http://hdl.handle.net/2117/23250
Pure bargaining problems and the Shapley rule
Carreras Escobar, Francisco; Owen Salazar, Guillermo
The developments over a thirty-year time span in the study of power, especially voting power, are traced in this book, which provides an up-to-date overview of applications of n-person game theory to the study of power in multimember bodies. Other theories that shed light on power distribution (e.g. aggregation theory) are treated as well. the book revisits the themes discussed in the well-known 1982 publication
Tue, 17 Jun 2014 13:52:14 GMThttp://hdl.handle.net/2117/232502014-06-17T13:52:14ZCarreras Escobar, FranciscoOwen Salazar, GuillermoThe developments over a thirty-year time span in the study of power, especially voting power, are traced in this book, which provides an up-to-date overview of applications of n-person game theory to the study of power in multimember bodies. Other theories that shed light on power distribution (e.g. aggregation theory) are treated as well. the book revisits the themes discussed in the well-known 1982 publicationPower, cooperation indices and coalition structures
http://hdl.handle.net/2117/23234
Power, cooperation indices and coalition structures
Amer Ramon, Rafael; Carreras Escobar, Francisco
The developments over a thirty-year time span in the study of power, especially voting power, are traced in this book, which provides an up-to-date overview of applications of n-person game theory to the study of power in multimember bodies. Other theories that shed light on power distribution (e.g. aggregation theory) are treated as well. the book revisits the themes discussed in the well-known 1982 publication
Mon, 16 Jun 2014 15:20:46 GMThttp://hdl.handle.net/2117/232342014-06-16T15:20:46ZAmer Ramon, RafaelCarreras Escobar, FranciscoThe developments over a thirty-year time span in the study of power, especially voting power, are traced in this book, which provides an up-to-date overview of applications of n-person game theory to the study of power in multimember bodies. Other theories that shed light on power distribution (e.g. aggregation theory) are treated as well. the book revisits the themes discussed in the well-known 1982 publicationOn the notion of dimension and codimension of simple games
http://hdl.handle.net/2117/11722
On the notion of dimension and codimension of simple games
Freixas Bosch, Josep; Marciniak, Dorota
Tue, 08 Mar 2011 16:04:26 GMThttp://hdl.handle.net/2117/117222011-03-08T16:04:26ZFreixas Bosch, JosepMarciniak, Dorota