Optimal sequential auctions

•Sequential first price and second-price procurement auctions are studied.•With substitutes the first-price auction achieves the low procurement cost.•With complements the second-price auction achieves the low procurement cost.•Bidders prefer the second-price auction when goods are substitutes.•Bidders prefer the first-price auction when goods are complements.

Sequential sealed first-price and open descending-price procurement auctions are studied. We examine which procurement auction rule achieves the low procurement cost. We show that the answer to this policy question depends on whether the items are complements or substitutes. With substitutes, the first-price procurement auction is preferred, while with complements, the open descending-price procurement auction is preferred. We also illustrate the procurement cost minimizing auction and the auction rule preferred by the bidders. With substitutes, bidders prefer the open descending-price procurement auction, while with complements bidders prefer the first-price procurement auction.