Emergence of social structures via preferential selection

We examine a weighted-network multiagent model with preferential selection such that agents choose partners with probability p (w), where w is the number of their past selections. When p (w) increases sublinearly with the number of past selections [p(w)∼w^α,α<1], agents develop a uniform preference for all other agents. At α =1, this state loses stability and more complex structures form. For a superlinear increase (α>1), strong heterogeneities emerge and agents make selections mainly within small and sometimes asymmetric clusters. Even in a few-agent case, the formation of such clusters resembles phase transitions with spontaneous symmetry breaking.