Abstract
We present a model of an Edgeworthian exchange economy where two goods are traded in a market place. For a specific class of random matching Edgeworthian economies, the expectation of the limiting equilibrium price coincides with that of related Walrasian economies. The novelty of our model is that we assign a bargaining skill factor to each participant which introduces a game, similar to the prisoner's dilemma, into the usual Edgeworth exchange economy. We analyze the effect of the bargaining skill factor on the amount of goods acquired and the overall increase in the utility of the consumer. Finally, we let the bargaining skills of the participants evolve with subsequent trades and study the impact of this change over time.

Abstract
Ourmain interest is to study the relevant biological thresholds that appear in epidemic and immunological dynamical models. We compute the thresholds of the SIRI epidemic models that determine the appearance of an epidemic disease. We compute the thresholds of a Tregs immunological model that determine the appearance of an immune response.

Abstract

Abstract
We present a simplified cycle model, using the available data, for the monthly sunspot number random variables {X-t}(t=1)(133), where 133 is taken as the mean duration of the Schwabe's cycle. We present a fit for the mean and standard deviation of X-t. In the descending and ascending phases, we analyse the probability histogram of the monthly sunspot number fluctuations.

Abstract
In this paper, we apply the following four power indices to the Portuguese Parliament: Shapley-Shubik index, Banzhaf index, Deegan-Packel index and Public Good Index. We also present the main concepts related with simple games and discuss the features of each power index by means of their axiomatic characterizations.

Abstract
Deegan and Packel (1979) and Holler (1982) proposed two power indices for simple games: the Deegan-Packel index and the Public Good Index. In the definition of these indices, only minimal winning coalitions are taken into account. Using similar arguments, we define two new power indices. These new indices are defined taking into account only those winning coalitions that do not contain null players. The results obtained with the different power indices are compared by means of two real-world examples taken from the political field.