Optimal auctions revisited

The Internet offers new challenges to the fields of economics and artificial intelligence. This paper addresses several basic problems inspired by the adaptation of economic mechanisms, and auctions in particular, to the Internet. Computational environments such as the Internet offer a high degree of flexibility in auctions' rules. This makes the study of optimal auctions especially interesting in such environments. Although the problem of optimal auctions has received a lot of attention in economics, only partial solutions are supplied in the existing literature. We present least upper bounds (l.u.b) R-n on the revenue obtained by a seller in any auction with n participants. Our bounds imply that if the number of participants is large then the revenue obtained by standard auctions (e.g., English auctions) approach the theoretical bound. Our results heavily rely on the risk-aversion assumption made in the economics literature. We further show that without this assumption, the seller's revenue (for a fixed number of participants) may significantly exceed the upper bound.