Consensus dynamics, network interaction, and Shapley indices in the Choquet framework

We consider a set $N = \{ 1,\ldots ,n \} of interacting agents whose individual opinions are denoted by x_{i} , i \in N in some domain {\mathbb {D}}\subseteq {\mathbb {R}} . The interaction among the agents is expressed by a symmetric interaction matrix with null diagonal and off-diagonal coefficients in the open unit interval. The interacting network structure is thus that of a complete graph with edge values in (0, 1). In the...