| Sumario: | Subsidy-free VCG mechanisms assign p identical objects to n agents. The efficiency loss is the largest ratio of budget surplus to efficient surplus, over all profiles of non-negative valuations. The smallest efficiency loss L[Graphic Character Omitted](n,p) satisfies L[Graphic Character Omitted](n,p)≤L[Graphic Character Omitted](n,[Graphic Character Omitted]n2[Graphic Character Omitted])≤43n. If pn is bounded away from 12, L[Graphic Character Omitted](n,p) converges to zero exponentially in n. Participation is voluntary in the optimal mechanism achieving L[Graphic Character Omitted](n,p) if p=1, but not if p≥2. Among voluntary mechanisms, the optimal efficiency loss is not significantly larger than L[Graphic Character Omitted](n,p) if pn≤12. But it does not converge to zero in n if pn>12. Copyright (c) 2008 Elsevier Inc.
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