Capítols de llibre
http://hdl.handle.net/2117/3434
2018-03-22T12:09:03ZPreorders 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.
This is a post-peer-review, pre-copyedit version of an article published in Lecture Notes in Computer Science. The final authenticated version is available online at: https://doi.org/10.1007/978-3-319-70647-4_5.
2018-01-31T10:31:34ZFreixas 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
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.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
2014-06-17T13:52:14ZCarreras 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
2014-06-16T15:20:46ZAmer 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
2011-03-08T16:04:26ZFreixas Bosch, JosepMarciniak, Dorota