Risk analysis sampling methods in terrorist networks based on the Banzhaf value.

This article introduces the Banzhaf and the Banzhaf-Owen values as novel measures of risk analysis of a terrorist attack, determining the most dangerous terrorists in a network. This new approach counts with the advantage of integrating at the same time the complete topology (i.e.

Lexicographic solutions for coalitional rankings.

In many real world situations, the design of social rankings over agents or items from a given raking over groups or coalitions, to which these agents or items belong to, is of big interest. With this aim, we revise the lexicographic excellence solution and introduce two novel solutions which, moreover, take into account the size of the groups. We present some desirable axioms which are interpreted in this context.

An application of the Shapley value to the analysis of co-expression networks.

We study the problem of identifying relevant genes in a co-expression network using a (cooperative) game theoretic approach. The Shapley value of a cooperative game is used to asses the relevance of each gene in interaction with the others, and to stress the role of nodes in the periphery of a co-expression network for the regulation of complex biological pathways of interest. An application of the method to the analysis of gene expression data from microarrays is presented, as well as a comparison with classical centrality indices.