Consumer-tracking technology offers new tools for price discrimination in digital markets. We examine the impact of sellers using this technology to adjust prices according to a buyer’s prior search length in a competitive search market where buyers differ in patience. We find “Coasian equilibria” wherein sellers reduce prices for buyers with longer search lengths which in turn requires them to reduce prices for buyers with shorter search lengths. In commonly studied environments, Coasian equilibria not only yield higher welfare for every buyer than all uniform-pricing equilibria, but are also the only equilibria when some mass of buyers are arbitrarily patient.