Universidad Carlos III de Madrid, Spain
Universidad Nacional de Educación a Distancia, Spain
Auctions have become a key mechanism in allocating items at different prices in many markets. Due to their special features and different formats, they are a useful tool for getting supply and demand to equilibrium. Some relevant markets where auctions are currently used are sales of personal communication services (PCSs), licenses, emission permits, electricity, and transportation services. It is very difficult to list the numerous papers on auctions but some examples are: Ref. 1 collects together in two volumes most of the relevant papers in the economics literature of auctions up to the year 2000; ref. 2 gives an account of developments in the field in the 40 years since Vickrey's pioneering paper; ref. 3 surveys the basic theory of how auctions work and describes the world-record-setting 3G mobile-phone license auctions; and ref. 4 gives an up-to-date treatment of both traditional theories of optimal auctions and newer theories of multiunit auctions and package auctions.
The study of auctions has traditionally been carried out by analytical means. However, this approach usually requires simplifying assumptions to reduce the complexity involved. This limitation is being tackled with ...