We study a simple duopoly model of preemption with multiple investments and instantaneous Bertrand competition in a stochastically growing market. Different patterns of equilibria may arise, depending on the importance of the real option effect. If the average growth rate of the market is close to the risk free rate, or if the volatility of demand changes is high, the unique equilibrium acquisition process involves joint adoption at the socially optimal date. If these conditions do not hold, the equilibrium investment timing is suboptimal, and the firms' long-run capacities depend on the initial market conditions. However, under a broad set of empirically relevant parameters, no dissipation of rents occur in equilibrium, despite instantaneous Bertrand competition. This casts some doubts on the robustness of one-shot models of preemption.