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## New paper on “Multi-Unit Auctions: Beyond Roberts”

My paper with Shahar Dobzinski titled Multi-Unit Auctions: Beyond Roberts, was just uploaded to the arXiv.

### Abstract

We exhibit incentive compatible multi-unit auctions that are not affine maximizers (i.e. are not of the VCG family) and yet approximate the social welfare to within a factor of $1+\epsilon$. For the case of two-item two-bidder auctions we show that this family of auctions, termed Triage mechanisms, are the only scalable ones that give an approximation factor better than 2. “Scalable” means that the allocation does not depend on the units in which the valuations are measured. We deduce from this that any scalable computationally-efficient incentive-compatible auction for $m$ items and $n \ge 2$ bidders cannot approximate the social welfare to within a factor better than 2. This is in contrast to arbitrarily good approximations that can be reached under computational constraints alone, and in contrast the optimal social welfare that can be obtained under incentive constraints alone.