We develop a simple model of retail competition in which retailers select prices and investments in cost reduction. Unable to observe firms' current prices prior to costly search, consumers monitor firms' historic pricing behavior. An equilibrium is constructed in which several identical firms enter and then engage in a phase of vigorous price competition, corresponding to a battle for low-price reputations. This phase is concluded with a "shakeout," as a low-price, low-cost firm comes to dominate the market while other firms lose market share. A central feature of the equilibrium is that low prices are complementary to large investments in cost reduction. Even though the dominant firm's price rises through time, and initially may be below marginal cost, we argue that an interpretation of predatory pricing may be appropriate, since the dominant firm is also the most-efficient (lowest-cost) firm in the market.