We study a competitive labor market with imperfect information. In our basic model, the labor market consists of heterogeneous workers and ex ante identical firms who have only imperfect private information about workers' productivities. Firms compete by posting wages in order to cherry-pick more productive workers from the applicant pool. The model predicts many important empirical regularities, including non-degenerated firm size distribution, persistent wage dispersion, and employer size-wage premium. We also consider extensions of the model where firms differ in either productivity or information about worker types, both generating assortative matching with a positive but imperfect correlation of worker and firm types. The main insight of this paper is that identical workers can get different wages depending on productivities of their coworkers in a competitive market with informational frictions. Our model also sheds light on inter-industry wage differential and sorting between industry and worker characteristics.