Combinatorial structures to modeling simple games and applications

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.Peer ReviewedPostprint (published version

Combinatorial structures to construct simple games and molecules

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.Peer ReviewedPostprint (published version

Coalitional power indices applied to voting systems

We describe voting mechanisms to study voting systems. The classical power indices applied to simple games just consider parties, players or voters. Here, we also consider games with a priori unions, i.e., coalitions among parties, players or voters. We measure the power of each party, player or voter when there are coalitions among them. In particular, we study real situations of voting systems using extended Shapley–Shubik and Banzhaf indices, the so-called coalitional power indices. We also introduce a dynamic programming to compute them.Peer ReviewedPostprint (published version

An Efficient generic algorithm for the generation of unlabelled cycles

In this report we combine two recent generation algorithms to obtain a new algorithm for the generation of unlabelled cycles. Sawada's algorithm lists all k-ary unlabelled cycles with fixed content, that is, the number of occurences of each symbol is fixed and given a priori. The other algorithm, by the authors, generates all multisets of objects with given total size n from any admissible unlabelled class A. By admissible we mean that the class can be specificied using atomic classes, disjoints unions, products, sequences, (multi)sets, etc. The resulting algorithm, which is the main contribution of this paper, generates all cycles of objects with given total size n from any admissible class A. Given the generic nature of the algorithm, it is suitable for inclusion in combinatorial libraries and for rapid prototyping. The new algorithm incurs constant amortized time per generated cycle, the constant only depending in the class A to which the objects in the cycle belong.Postprint (published version

Markov chains applied to Parrondo’s paradox: the coin tossing problem

Parrondo’s paradox was introduced by Juan Parrondo in 1996. In game theory, this paradox is described as: A combination of losing strategies becomes a winning strategy. At first glance, this paradox is quite surprising, but we can easily explain it by using simulations and mathematical arguments. Indeed, we first consider some examples with the Parrondo’s paradox and, using the software R, we simulate one of them, the coin tossing. Actually, we see that specific combinations of losing games become a winning game. Moreover, even a random combination of these two losing games leads to a winning game. Later, we introduce the major definitions and theorems over Markov chains to study our Parrondo’s paradox applied to the coin tossing problem. In particular, we represent our Parrondo’s game as a Markov chain and we find its stationary distribution. In that way, we exhibit that our combination of two losing games is truly a winning combination. We also deliberate possible applications of the paradox in some fields such as ecology, biology, finance or reliability theory.Peer ReviewedPostprint (published version

Help to new students of ICT Systems Engineering Degree at EPSEM-UPC: mentoring

Freshmen at the Manresa School of Engineering, Escola Politècnica Superior d'Enginyeria de Manresa (EPSEM), of the Universitat Politècnica de Catalunya (UPC) are voluntarily provided with the mentoring service during their initial period at University. Mentoring gives academic, teaching and self-organizational support. It improves academic results and reduces the percentage desertion of the studies. The mentor is usually an experimented student who is studying his last year’s Degree. The goal of the present work is to expose how mentoring is performanced in ICT (Information, Communication and Technology) Systems Engineering Degree at EPSEM. These studies have been recently created and they are unique in Spain (according to our knowledge). We present here a treatment and analysis of the performance and possible actions that have taking in account in order to continuous improvement. We have analyzed the methodology and the opinion of the Degree’s students during two academic years (2010-2011 and 2011-2012) in which mentoring was possible thanks to a Grant from EnginyCat AGAUR (Agency for Administration of University and Research Grants of “Generalitat de Catalunya”) and the UPC. Then, this Grant was unfortunately cancelled and mentoring could not go on. That’s why mentoring has been just applied few academic years, what is not enough to develop an exhaustive statistical analysis. However, we think that results are very interesting and we aim to carry on with this activity as soon as possible in order to develop more comprehensive resultsPeer Reviewe

Maximum tolerance and maximum greatest tolerance

An important consideration when applying neural networks is the sensitivity to weights and threshold in strict separating systems representing a linearly separable function. Two parameters have been introduced to measure the relative errors in weights and threshold of strict separating systems: the tolerance and the greatest tolerance. Given an arbitrary separating system we study which is the equivalent separating system that provides maximum tolerance or/and maximum greatest tolerance.Postprint (author’s final draft

Measuring satisfaction in societies with opinion leaders and mediators

An opinion leader-follower model (OLF) is a two-action collective decision-making model for societies, in which three kinds of actors are considered:Preprin

Cooperation through social influence

We consider a simple and altruistic multiagent system in which the agents are eager to perform a collective task but where their real engagement depends on the willingness to perform the task of other influential agents. We model this scenario by an influence game, a cooperative simple game in which a team (or coalition) of players succeeds if it is able to convince enough agents to participate in the task (to vote in favor of a decision). We take the linear threshold model as the influence model. We show first the expressiveness of influence games showing that they capture the class of simple games. Then we characterize the computational complexity of various problems on influence games, including measures (length and width), values (Shapley-Shubik and Banzhaf) and properties (of teams and players). Finally, we analyze those problems for some particular extremal cases, with respect to the propagation of influence, showing tighter complexity characterizations.Peer ReviewedPostprint (author’s final draft