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.