Asymptotically Optimal Multi-Object Auctions

A seller who wishes to sell a set of (distinct or similar) items can attempt to do it by a variety of auction mechanisms, such as combinatorial auctions, sequential auctions or parallel auctions. We provide a proof for the intuitive result that if the potential buyers are risk averse, then for every mechanism, the expected revenue of the seller in equilibrium is bounded above by the expected maximal surplus of the potential buyers, provided that the expected utility of every agent in this equilibrium is non negative. In our main result, we prove that if the number of potential buyers is sufficiently large and there are no externalities, then in the valuation-symmetric independent-private-values model, in which the valuation functions over allocations of items are independent across players, this upper bound is almost achieved by the Vickrey-Clarke [VC] mechanism. Hence, in an environment with many potential buyers, e.g., the Internet, a monopolist who uses the VC mechanism can extract almost all social surplus from the agents ∗We thank Steve Tadelis for very helpful discussions and remarks. Part of this work has been carried out while the second author was with the computer science department at Stanford university.