Simultaneous pooled auctions with multiple bids and preference lists

A simultaneous pooled auction with multiple bids and preference lists is a way to auction multiple heterogeneous objects to multiple bidders with unit demand. Bidders submit bids for every object, and a preference ordering over which object they would like to get if they have the highest bid on more than one object. This type of auction has been used in the Netherlands and in Ireland to auction available spectrum. We show that this type of auction does not satisfy elementary desirable properties such as the existence of an efficient equilibrium.