We explore patterns of price competition in an oligopoly where consumers vary in the set of firms they consider for their purchase and buy from the lowest‐priced firm they consider. We study a pattern of consideration, termed “symmetric interactions,” that generalizes models used in existing work (duopoly, symmetric firms, and firms with independent reach). Within this class, equilibrium profits are proportional to a firm's reach, firms with a larger reach set higher average prices, and a reduction in the number of firms (either by exit or by merger) harms consumers. However, increased competition (either by entry or by increased consumer awareness) does not always benefit consumers. We go on to study patterns of consideration with asymmetric interactions. In situations with disjoint reach and with nested reach, we find equilibria in which price competition is “duopolistic”: only two firms compete within each price range. We characterize the contrasting equilibrium patterns of price competition for all patterns of consideration in the three‐firm case.