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We study a labor market in which two identical firms compete over a pool of homogeneous workers. Firms pre‐commit to their outreach to potential employees, either through their informative advertising choices, or through their screening processes, before engaging in a wage (Bertrand) competition. Although firms are homogeneous, the unique pure‐strategy equilibrium is asymmetric: one firm maximizes its outreach whereas the other compromises on a significantly smaller market share. The features of the asymmetric equilibrium extend to a general oligopsony with any finite number of firms.