Optimal auctions revisited

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 auction's rules. This makes the study of optimal auctions especially interesting in such environments. We present an upper bound on the revenue obtained by a seller in any auction with a fixed number of participants, and we show that this bound may be a least upper bound in some setups. We further show that the revenue obtained by standard auctions (e.g., English auctions) approaches the theoretical bound, when the number of participants is large. 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 if the participants are sufficiently risk-seeking.