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We consider a labor market with search frictions in which firms need to invest in capital before they can post a vacancy. This assumption creates a natural scope for hold-up problems, but the innovation of our study is that we allow for competition among the applicants who apply for the same job. In our economy all applicants are paid their actual marginal product. Nonetheless, with random search there exists a hold-up problem, leading to underinvestment in capital. On the contrary, if workers can direct their search towards firms with different capital levels, the equilibrium is efficient. This result contrasts sharply with the predictions of models with ex-post bargaining that never yield an efficient allocation. Moreover, our results extend the efficiency of auction mechanisms to an environment with non-contractible investments.