This dissertation deals with the problem bidders have to solve to formulate their bids in two types of auctions: reverse and combinatorial auctions.

In reverse procurement auctions the object for sale is a contract, bidders are suppliers, and the bid taker is a buyer. The suppliers bidding for the contract are usually the current supplier (the incumbent) and a group of potential new suppliers (the entrants). Since the buyer has an ongoing relationship with the incumbent, he needs to adjust the bids of the entrants to include non-price attributes. The buyer can run a scoring auction, in which suppliers compete on the adjusted bids or scores, or, he can run a buyer-determined auction, in which suppliers compete on the price, and the buyer adjusts the bids with the non-price attributes after the auction to determine the winner. In the second chapter I study the bidding strategies in a buyer-determined auction in which an incumbent and a group of suppliers compete for a contract.

When diff erent types of suppliers compete (for example domestic and foreign suppliers), practitioners have observed that domestic suppliers stop bidding after observing a low bid from the foreign competitors, even though the domestic suppliers dominate their foreign competitors in non-price dimensions. To mitigate this anticompetitive behavior, the feedback given to suppliers in the auction changed from the bid price to the bid rank. In the third chapter, I study the bidding strategies when two suppliers of diff erent type compete in a reverse auction with rank feedback.

Finally, in the fourth chapter, I study the bidding strategies in sealed-bid combinatorial auctions. Combinatorial auctions are auctions of multiple heterogeneous objects that allow bids on subsets of the objects, giving bidders the exibility to express if the objects in a set are more valuable together than separate. This added exibility makes it possible for the bidders to express a variety of preferences, but also complicates the problem they need to solve to find their bidding strategies. I present the problem a bidder has to solve in a combinatorial auction of two objects, in which bidders submit mutually exclusive bids once and winners pay their bids.