Strong Random Correlations In Networks of Heterogeneous Agents

Correlations and other collective phenomena are considered in a schematic model of pairwise interacting, competing and collaborating agents facing a binary choice and situated at the nodes of the complete graph and a two-dimensional regular lattice, respectively. The agents may be subjected to an idiosyncratic or common external influence and also some random noise. The system's stochastic dynamics is studied by numerical simulations. It displays the characteristics of punctuated, multiple equilibria, sensitivity to small details, and path dependence. The dynamics is so slow that one can meaningfully speak of quasi-equilibrium states. Performing measurements of correlations between the agents' choices we find that they are random both as to their sign and absolute value, but their distribution is very broad when the interaction dominates both the noise and the external field. This means that random but strong correlations appear with large probability. In the two dimensional model this also implies that the correlations on average fall off with distance very slowly: the system is essentially non-local, small changes at one end may have a strong impact at the other. The strong, random correlations tend to organize a large fraction of the agents into strongly correlated clusters that act together. If we think of this model as a metaphor of social or economic agents or bank networks, the systemic risk implications of this tendency are clear: any impact on even a single strongly correlated agent will not be confined to a small set but will spread, in an unforeseeable manner, to the whole system via the strong random correlations