Multi-Unit Auction Revenue with Possibilistic Beliefs

Abstract

The revenue of traditional auction mechanisms is benchmarked solely against the players' own valuations, despite the fact that they may also have valuable beliefs about each other's valuations. Not much is known about generating revenue in auctions of multiple identical copies of a same good. (In particular the celebrated Vickrey mechanism has no revenue guarantees.) For such auctions, we (1) put forward an attractive revenue benchmark, based on the players' possibilistic about each other, and (2) construct a mechanism that achieves such benchmark, assuming that the players are two-level rational (where the rationality is in the sense of Aumann).