We explore patterns of price competition in an oligopoly where consumers vary in the set of suppliers they consider for their purchase. In the case of "nested reach" we find equilibria, unlike those in existing models, in which price competition is segmented: small firms offer only low prices and large firms only offer high prices. We characterize equilibria in the three-firm case using correlation measures of interaction between pairs of firms. We show how entry, merger and market expansion can affect patterns of price competition in novel ways