Abstract
We construct a variant of the Vickrey auction of a single object where the surplus is split in exogenously fixed shares between the seller and the buyers, up to a margin of error vanishingly exponentially as the number of buyers grows. When the object is the common property of the participants, we can similarly construct VCG mechanisms with a vanishingly small cash transfer to the residual claimant. For any integer q, 3 ≤ q ≤ n, we find the mechanism guaranteeing to each participant a fair share of the qth highest valuation, while minimizing the worst possible ratio of the cash transfer to the efficient surplus. We perform a parallel analysis when the object is undesirable. We compare the cash lost to the largest spread between individual valuations, and obtain the same trade-offs between fairness and the relative loss of surplus.
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This work was supported by the NSF under Grant SES-0414543. Several conversations with Geoffroy de Clippel are gratefully acknowledged.
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Moulin, H. Auctioning or assigning an object: some remarkable VCG mechanisms. Soc Choice Welf 34, 193–216 (2010). https://doi.org/10.1007/s00355-009-0393-5
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DOI: https://doi.org/10.1007/s00355-009-0393-5