This paper considers a simple equilibrium model of an imperfectly competitive two-sided matching market. Firms and workers may have heterogeneous preferences over matches on the other side, and the model allows for both uniform and personalized wages or contracts. To make the model tractable, I use the Azevedo and Leshno (2013) framework, in which a finite number of firms is matched to a continuum of workers. In equilibrium, even if wages are exogenous and fixed, firms have incentives to strategically reduce their capacity, to increase the quality of their worker pool. The intensity of incentives to reduce capacity is given by a simple formula, analogous to the classic Cournot model, but depends on different moments of the distribution of preferences. I compare markets with uniform and personalized wages. For fixed quantities, markets with personalized wages always yield higher efficiency than markets with uniform wages, but may be less efficient if firms reduce capacity to avoid bidding too much for star workers.