Oligopolistic competition in price and quality

We consider an oligopolistic market where firms compete in price and quality and where consumers are heterogeneous in knowledge: some consumers know both the prices and quality of the products offered, some know only the prices and some know neither. We show that two types of signalling equilibria are possible. Both are characterised by dispersion and Pareto-inefficiency of the price/quality offers. But, better price/quality combinations are signalled with lower prices in one type and with higher prices in the other type.