Growth and Defection in Hierarchical, Synergistic Networks

Certain classes of social and economic networks display a set of fundamentally similar characteristics: individuals benefit from being in groups, and the groups are internally organized in a hierarchical fashion where benefit is allocated unequally. To better understand how these networks evolve and maintain themselves, we developed a model that grows hierarchical networks through the local actions of agents who can both solicit others to join their group and defect to start their own independent organization. Group benefit is conceptualized as synergy, which increases more rapidly than the sum of the individual talent of group members. Synergy is allocated back to members within the hierarchy through a nonlinear payback function such that the higher an individual is within the hierarchy, the greater their payback. Parametric simulations where we consider the influence of the payback function and population size indicate that cluster size transitions from the size of the entire population where the maximum system synergy is obtained to smaller and smaller values as payback becomes increasingly inequitable and population size becomes large. For such sub-maximal situations, we find cluster size and total system synergy to fluctuate with well defined mean values that suggests the existence of a stochastically stable, asymptotic attractor.