We show how to numerically solve for a Markov-perfect equilibrium of a dynamic auction game where a procurer repeatedly purchases construction services from capacity-constrained firms. We find that the procurer is best off scheduling frequent auctions for small project sizes. Otherwise, firm capacity utilization rates become larger and more asymmetric, which softens competition and increases procurement costs. We also find that forward-looking bidding dampens the competition-softening effects of asymmetry: farsighted firms compete more intensely than myopic ones. This can undermine the goal of a bid-preference-style affirmative action program: more farsighted firms respond less to the asymmetry induced via bid preferences.