Emergence of Social Structures via Preferential Selection

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