Social activity and network formation

This paper develops a simple model in which a social hierarchy emerges endogenously when agents form a network for complementary interaction (``activity''). Specifically, we assume that agents are ex ante identical and their best response activity, as well as their value function, increases (strictly) concavely in the total activity of their neighbours in the network. There exists a unique and stable positive activity equilibrium on exogenous networks under mild conditions. When we endogenise network formation, equilibria become strongly structured: more active players have more neighbours, i.e. a higher degree, but tend to sponsor fewer links. Additionally, in strict equilibria agents separate themselves into groups characterised by the symmetric activity of their members. The characteristic activity decreases in group size and the network is a complete multipartite graph.