Multi-unit auctions: Beyond Roberts

We then proceed to characterizing ex-post implementable social choice functions that are approximately efficient. For the case of two-item two-bidder auctions, we show that triage auctions are the only scalable ex-post implementable social choice functions that always output a solution with value greater than half of the value of the efficient allocation. “Scalable” means that the allocation does not depend on the units (the “currency”) in which the valuations are measured. We use the two-item characterization to provide an almost complete description of all scalable ex-post implementable social choice functions for any number of items and show that they usually identify with triage auctions.