A continuous model of strong and weak ties

Abstract

When individuals interact in a network, links are often asymmetric and of varying intensity. I study a model whereby networks emerge from agents maximizing utility from continuous linking decisions and self-investment. The joint link surplus function allows arbitrary, bounded heterogeneity in the benefit to forming links. Under decreasing returns to scale in link surplus, the set of Nash equilibria is well-behaved. In contrast, with constant or increasing returns to scale, heterogeneity and returns to self-investment limit the set of Nash equilibria. This model rationalizes equilibrium networks in which individuals simultaneously hold ties that are asymmetric and of varying intensity.