Emergence of Social Structures via Preferential Selection

TL;DR

This paper investigates how social structures emerge in a multi-agent network model based on preferential selection, revealing phase transitions and cluster formations depending on the growth rate of selection probability.

Contribution

It introduces a weighted-network multi-agent model with a novel preferential selection mechanism and analyzes the resulting phase transitions and cluster formations.

Findings

Uniform preference for all agents when $p(w)$ increases sublinearly.

Complex structures and heterogeneities emerge at critical points.

Cluster formation resembles phase transitions with symmetry breaking.

Abstract

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.