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We propose a simple theory of predatory pricing based on incumbency advantages, scale economies, and sequential buyers (or markets). The prey needs a critical scale to be successful. The incumbent (or predator) has an initial advantage and is ready to make losses on earlier buyers to deprive the prey of the scale it needs, thus making monopoly profits on later buyers. Several extensions are considered, including cases in which scale economies exist because of demand externalities or two-sided market effects and in which markets are characterized by common costs. Conditions under which predation may (or may not) take place in actual cases are also discussed.