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This paper analyses a model of strategic exploration in which competing players independently explore a set of alternatives. The model features a multiple-player multiple-armed bandit problem and captures a strategic trade-off between pre-emption—covert exploration of alternatives that the opponent will explore in the future—and prioritization—exploration of the most promising alternatives. Our results explain how the strategic trade-off shapes equilibrium behaviours and outcomes, for example, in technology races between superpowers and R&D competitions between firms. We show that players compete on the same set of alternatives, leading to duplicated exploration from start to finish, and they explore alternatives that are a priori less promising before more promising ones are exhausted. The model also predicts that competition induces players to implement unreliable technologies too early, even though they should wait for the technologies to mature. Coordinated exploration is impossible even if the alternatives are equally promising, but it can emerge in equilibrium following a phase of pre-emptive competition if there is a short deadline. With asymmetric capacities of exploration, the weak player conducts extensive instead of intensive exploration—exploring as many alternatives as the strong player does but never fully exploring any.