The paper introduces a class of alternating-move infinite-horizon models of duopoly. The timing is meant to capture the presence of short-run commitments. Markov perfect equilibrium (MPE) in this context requires strategies to depend only on the action to which one's opponent is currently committed. The dynamic programming equations for an MPE are derived. The first application of the model is to a natural monopoly, in which fixed costs are so large that at most one firm can make a profit. The firms install short-run capacity. In the unique symmetric MPE, only one firm is active and practices the quantity analogue of limit pricing. For commitments of brief duration, the market is almost contestable. We conclude with a discussion of more general models in which the alternating timing is derived rather than imposed. Our companion paper applies the model to price competition and provides equilibrium foundations for kinked demand curves and Edgeworth cycles.