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### Paper:

TR09-068 | 1st September 2009 23:17

#### Limits on the Social Welfare of Maximal-In-Range Auction Mechanisms

TR09-068
Authors: Dave Buchfuhrer, Chris Umans
Publication: 1st September 2009 23:34
Many commonly-used auction mechanisms are maximal-in-range''. We show that any maximal-in-range mechanism for $n$ bidders and $m$ items cannot both approximate the social welfare with a ratio better than $\min(n, m^\eta)$ for any constant $\eta < 1/2$ and run in polynomial time, unless $NP \subseteq P/poly$. This significantly improves upon a previous bound on the achievable social welfare of polynomial time maximal-in-range mechanisms of $2n/(n+1)$ for constant $n$. Our bound is tight, as a $\min(n,2m^{1/2})$ approximation of the social welfare is achievable.