Procurement auctions with capacity constrained suppliers

•Characterize asymmetric bidding equilibrium in pay-as-bid procurement auction.•Provide comparative statics on the bidding equilibrium.•Provide an open auction implementation when suppliers have capacity constraints.•Open auction format is optimal and gives lower expected cost than sealed auction.

In this paper we study two reverse auction formats in a single period setting, the sealed pay-as-bid and the open format, when suppliers are capacity constrained. In the pay-as-bid format we characterize the asymmetric bidding equilibrium for the case of two suppliers with uniformly distributed cost. We find that the pay-as-bid auction allocates business inefficiently and that a supplier’s bid is nonincreasing in the opponent’s capacity and is typically decreasing in its own capacity. We then characterize a descending price-clock open auction implementation and find that it is optimal and that the buyer’s expected cost decreases as capacity is more evenly spread. Finally, we find that the pay-as-bid auction results in a higher expected cost to the buyer as compared to the open auction.