We study the impact of strategic behavior in labor markets characterized by algorithmic monoculture, where firms compete for a shared pool of applicants using a common algorithmic evaluation. In this setting, "naive" hiring strategies lead to severe congestion, as firms collectively target the same high-scoring candidates. We model this competition as a game with capacity-constrained firms and fully characterize the set of Nash equilibria. We demonstrate that equilibrium strategies, which naturally diversify firms' interview targets, significantly outperform naive selection, increasing social welfare for both firms and applicants. Specifically, the Price of Naive Selection (welfare gain from strategy) grows linearly with the number of firms, while the Price of Anarchy (efficiency loss from decentralization) approaches 1, implying that the decentralized equilibrium is nearly socially optimal. Finally, we analyze convergence, and we show that a simple sequential best-response process converges to the desired equilibrium. However, we show that firms generally cannot infer the key input needed to compute best responses, namely congestion for specific candidates, from their own historical data alone. Consequently, to realize the welfare gains of strategic differentiation, algorithmic platforms must explicitly reveal congestion information to participating firms.