  We study the diffusion of a true and a false message (the rumor) in a social
network. Upon hearing a message, individuals may believe it, disbelieve it, or
debunk it through costly verification. Whenever the truth survives in steady
state, so does the rumor. Communication intensity in itself is irrelevant for
relative rumor prevalence, and the effect of homophily depends on the exact
verification process and equilibrium verification rates. Our model highlights
that successful policies in the fight against rumors increase individuals'
incentives to verify.
