We consider in this paper competition through prices and market coverages in a spatial duopoly. We characterize and compare the Stackelberg equilibria and the Bertrand equilibria. We show that when the cost of informing the consumers is small, duopolists always choose to inform all consumers in the Bertrand equilibrium but the leader in the Stackelberg equilibrium may choose not to inform everyone when the duopolistic competition is intense enough (thereby generating overlapping markets). In equilibrium, prices may be strategic complements, strategic substitutes or be strategically independent. Considering market coverage as chosen by the firms changes the 'conventional' relationships between differentiation, profits and markups.