"Diffusion on a Sorted Network"

We study the diffusion of a disease or information in an endogenous network consisting of heterogeneous individuals. Individuals differ by the cost (value) of infection (information), or by their frequency of meeting others. Moreover, individuals realize an idiosyncratic match value before deciding whether to match.  We characterize the equilibrium using a system of linear differential equations with time-varying coefficients. We show strategic complementarity in matching: when others are more likely to accept a match, the marginal utility from matching with others for each individual also increases. This strategic complementarity endogenously generates sorting by infection probability, return, and contact rates. This sorting endogenously slows down the transmission of an infectious disease and accelerates the diffusion of information.