Using coalitional games on biological networks to measure centrality and power of genes

Abstract Motivation: The interpretation of gene interaction in biological networks generates the need for a meaningful ranking of network elements. Classical centrality analysis ranks network elements according to their importance but may fail to reflect the power of each gene in interaction with the others. Results: We introduce a new approach using coalitional games to evaluate the centrality of genes in networks keeping into account genes' interactions. The Shapley value for coalitional games is used to express the power of each gene in interaction with the others and to stress the centrality of certain hub genes in the regulation of biological pathways of interest. The main improvement of this contribution, with respect to previous applications of game theory to gene expression analysis, consists in a finer resolution of the gene interaction investigated in the model, which is based on pairwise relationships of genes in the network. In addition, the new approach allows for the integration of a priori knowledge about genes playing a key function on a certain biological process. An approximation method for practical computation on large biological networks, together with a comparison with other centrality measures, is also presented. Contact: [email protected]

Exploiting the Shapley Value in the Estimation of the Position of a Point of Interest for a Group of Individuals

Concepts and tools from cooperative game theory are exploited to quantify the role played by each member of a team in estimating the position of an observed point of interest. The measure of importance known as “Shapley value” is used to this end. From the theoretical point view, we propose a specific form of the characteristic function for the class of cooperative games under investigation. In the numerical analysis, different configurations of a group of individuals are considered: all individuals looking at a mobile point of interest, one of them replaced with an artificially-generated one who looks exactly toward the point of interest, and directions of the heads replaced with randomly-generated directions. The corresponding experimental outcomes are compared

A social capital index

In this paper we propose a social capital measure for individuals belonging to a social network. To do this, we use a game theoretical approach and so we suppose that these individuals are also involved in a cooperative TU-game modelling the economic or social interests that motivate their interactions. We propose as a measure of individual social capital the difference between the Myerson and the Shapley values of actors in the social network and explore the properties of such a measure. This definition is close to our previous measure of centrality (Gómez et al., 2003) and so in this paper we also study the relation between social capital and centrality, finding that this social capital measure can be considered as a vector magnitude with two additive components: centrality and positional externalities. Finally, several real political examples are used to show the agreement of our conclusions with the reality in these situations