Multi-object Auctions: On the Use of Combinational Bids

This paper studies multiple object auctions when there are two kinds of bidders: those interested in the bundle being sold (bundle bidders) and those that want one specific object only (unit bidders). The analysis has been motivated by the sale of spectrum rights in the United States.Using a simple model of independent valuations I explore the properties of the optimal auction and its implementation. I show that an optimal mechanism requires combinational bids for the bundle and for each of the units. Moreover, if the optimal mechanism allocates the objects efficiently, a combination of second-price auctions allows the implementation of the optimal mechanism, while a combination of first-price auctions does not.