GRTJ - Grup de Recerca en Teoria de Jocs
http://hdl.handle.net/2117/3429
2015-10-09T03:55:58ZForms of representation for simple games: Sizes, conversions and equivalences
http://hdl.handle.net/2117/77521
Forms of representation for simple games: Sizes, conversions and equivalences
Molinero Albareda, Xavier; Riquelme Csori, Fabián; Serna Iglesias, María José
Simple games are cooperative games in which the benefit that a coalition may have is always binary, i.e., a coalition may either win or loose. This paper surveys different forms of representation of simple games, and those for some of their subfamilies like regular games and weighted games. We analyze the forms of representations that have been proposed in the literature based on different data structures for sets of sets. We provide bounds on the computational resources needed to transform a game from one form of representation to another one. This includes the study of the problem of enumerating the fundamental families of coalitions of a simple game. In particular we prove that several changes of representation that require exponential time can be solved with polynomial-delay and highlight some open problems.
2015-07-01T00:00:00ZMeasuring the relevance of factors in the occurrence of events
http://hdl.handle.net/2117/76392
Measuring the relevance of factors in the occurrence of events
Fragnelli, Vito; Freixas Bosch, Josep; Pons Vallès, Montserrat; Sanmiquel Pera, Lluís
A new way to compare the relevance of the different factors intervening in the occurrences of an event is presented and developed in this paper. The idea behind the method comes from cooperative game theory but the focus is slightly different because factors are not necessarily rational decision-makers and because the only data available are obtained by repetition of the event. The concept of relevance measure for a factor in a set of data is introduced, some significant examples are given and the main properties of relevance measures are defined and studied. One of these measures, the fair measure, is proved to have interesting properties which characterize it. Two real world situations, one about traffic accidents and the other one about mining accidents, both of them with real data, are used to show the use of relevance measures to compare factors in each one of these events.
2014-05-09T00:00:00ZSuccess and decisiveness on proper symmetric games
http://hdl.handle.net/2117/76379
Success and decisiveness on proper symmetric games
Freixas Bosch, Josep; Pons Vallès, Montserrat
This paper provides a complete study for the possible rankings of success and decisiveness
for individuals in symmetric voting systems, assuming anonymous and independent
probability distributions. It is proved that for any pair of symmetric voting
systems it is always possible to rank success and decisiveness in opposite order whenever
the common probability of voting for “acceptance” is big enough. On the contrary, for
probability values lower than one–half it is not possible to reverse the ranking of these
two measures.
2013-11-20T00:00:00ZOn the time decay of solutions in micropolar viscoelasticity
http://hdl.handle.net/2117/76207
On the time decay of solutions in micropolar viscoelasticity
Leseduarte Milán, María Carme; Magaña Nieto, Antonio; Quintanilla de Latorre, Ramón
This paper deals with isotropic micropolar viscoelastic materials.
It can be said that that kind of materials have two internal structures: the
macrostructure, where the elasticity effects are noticed, and the microstructure,
where the polarity of the material points allows them to rotate. We introduce,
step by step, dissipation mechanisms in both structures, obtain the corresponding
system of equations and determine the behavior of its solutions with respect the
time.
The final publication is available at Springer via http://dx.doi.org/10.1007/s11012-015-0117-0
2015-07-01T00:00:00ZThe golden number and Fibonacci sequences in the design of voting structures
http://hdl.handle.net/2117/28263
The golden number and Fibonacci sequences in the design of voting structures
Freixas Bosch, Josep; Kurz, Sascha
Some distinguished types of voters, as vetoes, passers or nulls, as well as some others, play a significant role in voting systems because they are either the most powerful or the least powerful voters in the game independently of the measure used to evaluate power. In this paper we are concerned with the design of voting systems with at least one type of these extreme voters and with few types of equivalent voters. With this purpose in mind we enumerate these special classes of games and find out that its number always follows a Fibonacci sequence with smooth polynomial variations. As a consequence we find several families of games with the same asymptotic exponential behavior except for a multiplicative factor
which is the golden number or its square. From a more general point of view, our studies are related with the design of voting structures with a predetermined importance ranking.
2013-01-01T00:00:00ZEgalitarian property for power indices
http://hdl.handle.net/2117/28262
Egalitarian property for power indices
Freixas Bosch, Josep; Marciniak, Dorota
In this study, we introduce and examine the Egalitarian property for some power indices on the class of simple games. This property means that after intersecting a game with a symmetric or anonymous game the difference between the values of two comparable players does not increase. We prove that the Shapley–Shubik index, the absolute Banzhaf index, and the Johnston score satisfy this property. We also give counterexamples for Holler, Deegan–Packel, normalized Banzhaf and Johnston indices. We prove that the Egalitarian property is a stronger condition for efficient power indices than the Lorentz domination.
2013-01-01T00:00:00ZA note on multinomial (probabilistic) values
http://hdl.handle.net/2117/28244
A note on multinomial (probabilistic) values
Domènech Blázquez, Margarita; Giménez Pradales, José Miguel; Puente del Campo, María Albina
The work tries to contribute to a better understanding of multinomial values as a consistent alternative or complement to classical values (Shapley and Banzhaf). We compare the behavior of multinomial values with respect several standard properties for values and power indices, including marginal contributions, balanced contributions, desirability relation and null player exclusion property.
2015-01-01T00:00:00ZThe proportional partitional Shapley value
http://hdl.handle.net/2117/27972
The proportional partitional Shapley value
Alonso Meijide, José María; Carreras Escobar, Francisco; Costa Bouzas, Julián; García Jurado, Ignacio
A new coalitional value is proposed under the hypothesis of isolated unions. The main
difference between this value and the Aumann–Drèze value is that the allocations within
each union are not given by the Shapley value of the restricted game but proportionally
to the Shapley value of the original game. Axiomatic characterizations of the new value,
examples illustrating its application and a comparative discussion are provided.
2015-05-01T00:00:00ZCoalitional multinomial probabilistic values
http://hdl.handle.net/2117/27632
Coalitional multinomial probabilistic values
Carreras Escobar, Francisco; Puente del Campo, María Albina
We introduce a new family of coalitional values designed to take into account players’ attitudes with regard to cooperation. This new family of values applies to cooperative games with a coalition structure by combining the Shapley value and the multinomial probabilistic values, thus generalizing the symmetric coalitional binomial semivalues. Besides an axiomatic characterization, a computational procedure is provided in terms of the multilinear extension of the game and an application to the Catalonia Parliament, Legislature 2003–2007, is shown.
2015-08-01T00:00:00ZOn the complexity of exchanging
http://hdl.handle.net/2117/27400
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.
2015-03-24T00:00:00Z