A group of n "quacks"plays a price-competition game, facing a continuum of "patients"who recover with probability α, whether they acquire a quack's "treatment". If patients chose rationally, the market would be inactive. I assume, however, that patients choose according to a boundedly rational procedure, which reflects "anecdotal"reasoning. This element of bounded rationality has significant implications. The market for quacks is active, and patients suffer a welfare loss which behaves non-monotonically w.r.t. n and α. In an extended model that endogenizes the quacks'choice of "treatments", the quacks minimize the force of price competition by offering maximally differentiated treatments. The patients'welfare loss is robust to market interventions, which would crowd out low-quality firms in standard models. Thus, as long as the patients'quality of reasoning is not lifted above the anecdotal level, ordinary competition policies may be ineffective.