Procurement auctions with ex post cooperation between capacity constrained bidders

The use of procurement auctions is a common practice for firms to procure goods and services. In this paper, we consider a first-price sealed-bid procurement auction consisting of two bidders with limited capacities. Each bidder is not able to complete the auctioned project on its own due to its capacity constraint. Upon the auction ends, the winning bidder has the option of cooperating with the losing bidder to fulfill the project. We investigate how the ex post cooperation affects bidders' bidding strategies and equilibrium profits as well as the competition intensity of the auction. Surprisingly, we find that a bidder's profit at equilibrium may decrease in its capacity level and increase in its unit cost. This is because a bidder's larger capacity or smaller unit cost would lower the other bidder's cost to complete the project due to the presence of cooperation, and thus intensify the competition between bidders. We also find that the winning bid price may become higher or lower (depending on bidders' characteristics) when bidders have the option of ex post cooperation. Further, it is shown that the bidder with a cost advantage may be hurt by the ex post cooperation.