A three-part tariff refers to a pricing scheme consisting of a fixed fee, a free allowance of units up to which the marginal price is zero, and a positive per-unit price for additional demand beyond that allowance. The three-part tariff and its variations are commonly used in both final-goods and intermediate-goods markets. Recently, the offering of three-part tariffs and the like by dominant firms has become a prominent antitrust issue. Existing studies have focused on monopoly models, interpreting the three-part tariff as a price discrimination device. In this paper, I investigate the strategic effects of three-part tariffs in a sequential-move game and offer an equilibrium theory of three-part tariffs in a competitive context. I show that, compared with linear pricing equilibrium and two-part tariff equilibrium, a three-part tariff always strictly increases the dominant firm's (the leader's) profit when competing against a rival (the follower) with substitute products, in the absence of usual price discrimination motive. To explore the effects of a three-part tariff on welfare, I further perform comparative statics analysis using general differentiated linear demand system. I show that the competitive effect of a three-part tariff in contrast to linear pricing depends on the degree of substitutability between products: Competition is intensified when two products are more differentiated, yet softened when two products are more substitutable. This is in stark contrast with the competitive scenario posed by a two-part tariff: A two-part tariff always enhances competition and gives the highest total surplus of these three pricing schemes. Moreover, the rival firm always gets hurt in both profit and quantity sale when the dominant firm switches from linear pricing to a two-part tariff, yet it enjoys higher profit when the dominant firm moves from a two-part tariff to the more ornate three-part tariff, despite the fact that its quantity and market share are decreased even further. My findings offer a new perspective on three-part tariffs, a perspective which could help antitrust enforcement agencies distinguish the exclusionary three-part tariff from the procompetitive one.