Abstract
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 ˆ ( n , p ) satisfies L ˆ ( n , p ) ⩽ L ˆ ( n , ⌊ n 2 ⌋ ) ⩽ 4 3 n . If p n is bounded away from 1 2 , L ˆ ( n , p ) converges to zero exponentially in n. Participation is voluntary in the optimal mechanism achieving L ˆ ( n , p ) if p = 1 , but not if p ⩾ 2 . Among voluntary mechanisms, the optimal efficiency loss is not significantly larger than L ˆ ( n , p ) if p n ⩽ 1 2 . But it does not converge to zero in n if p n > 1 2 .
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