We analyze models of product differentiation with perfect price discrimination and free entry. With a fixed number of firms, and in the absence of coordination failures, perfect price discrimination provides incentives for firms to choose product characteristics in a socially optimal way....

In signalling environments ranging from consumption to education, high-quality senders often shun the standard signals that should separate them from lower-quality senders. We find that allowing for additional, noisy information on sender quality permits equilibria where medium types signal to...