How do Interactions Influence Formation of Social Networks? A General Microfounded Explanation

This paper investigates the strategic interaction effects that precede network formation. We find that for a general class of payoff functions which, among other things, feature strict supermodularity, the degree of a node is a sufficient statistic for the action it undertakes. Dynamically, we construct a general model where each period consists of two stages: first, a game on the given network is played and second, a link is either created or severed. It turns out that the payoff functions we consider give absolute convergence to the absorbing class of networks called nested split graphs. These networks do not only possess mathematically tractable characteristics, but we can also interpret real-world networks as perturbed nested split graphs. The general framework provided here can be applied to more or less complex models of network formation.