Oligopolistic competition in price and quality

We consider an oligopolistic market where firms compete in price and quality and where consumers have heterogeneous information: some consumers know both the prices, and quality of the products offered, some know only the prices, and some know neither. We show that if there are sufficiently many uninformed consumers, then there exists a unique equilibrium where price is a perfect indicator of quality. This equilibrium is characterized by dispersion and Pareto-inefficiency of the price/quality offers, where better price/quality combinations are associated with lower prices.