Asymmetric market power and wage suppression

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.