Strategic implications of the learning curve hypothesis are analyzed in a model of a price-setting, differentiated duopoly selling to a sequence of heterogeneous buyers with uncertain demands. A unique and symmetric Markov perfect equilibrium is characterized, and two concepts of self-reinforcing market dominance investigated. One is increasing dominance (ID), whereby the leading firm has a greater probability of winning the next sale; the other is increasing increasing dominance (IID), whereby a firm's probability of winning the next sale increases with the length of its lead. Sufficient conditions for IID (and thus for ID) are that the discount factor is sufficiently low or sufficiently high. Other sufficient conditions for ID and IID are given in the case of two-step learning, in which a firm reaches the bottom of its learning curve after just two sales. However, examples are also constructed for the two-step learning case in which neither ID nor IID holds. It is also shown that, in equilibrium, IID implies that learning is privately disadvantageous, although it is socially advantageous. Finally, introducing avoidable fixed costs and possible exit into the model yields a new theory of predatory pricing based on the learning curve hypothesis.