Auctions
Optimal design

A special feature of the auction of spectrum licenses for personal communication services in the US was that while some operators only wanted to work at the local level (thus only demanding a single license), others were interested in aggregating several licenses to serve a broader area. Some theoretical models suggest that if in addition to bidding for single licenses, operators are allowed to bid for aggregates of licenses, the final allocation will tend to be inefficient, and that dealing with this problem involves mechanisms that are far too complex. As a consequence of this view, the US ran independent auctions. In Discussion Paper No. 1216, Research Affiliate Fernando Branco aims to shed some light on these issues, using a simple model involving two goods, two buyers who each want to buy only one good, and one buyer (B) who wants to buy the bundle of both goods.

The author explores how these two objects should be sold to maximize the seller's revenue, identifying optimal allocation rules that show that it is never the case that the seller should allocate a single object to buyer B. This conclusion demonstrates that running independent auctions, which may leave B with one object, are sub-optimal. More specifically, the author finds that a second-price combinational bid process allocates the objects efficiently and is an optimal mechanism. The first-price combinational auction is not an optimal mechanism because of the externalities that the bidders for the single objects exert on each other.

Multi-object Auctions: On the Use of Combinational Bids
Fernando Branco

Discussion Paper No. 1216, August 1995 (IO)