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On the Fastest Vickrey Algorithm

Abstract

We investigate the algorithmic performance of Vickrey-Clarke-Groves mechanisms in the single item case. We provide a formal definition of a Vickrey algorithm for this framework, and give a number of examples of Vickrey algorithms. We consider three performance criteria, one corresponding to a Pareto criterion, one to worst-case analysis, and one related to first-order stochastic dominance. We show that Pareto best Vickrey algorithms do not exist and that worst-case analysis is of no use in discriminating between Vickrey algorithms. For the case of two bidders, we show that the bisection auction stochastically dominates all Vickrey algorithms. We extend our analysis to the study of weak Vickrey algorithms and winner determination algorithms. For the case of two bidders, we show that the One-Search algorithm stochastically dominates all column monotonic weak Vickrey algorithms and that a suitably adjusted version of the bisection algorithm, the WD bisection algorithm, stochastically dominates all winner determination algorithms. The WD bisection algorithm Pareto dominates all column monotonic winner determination algorithms in the n bidder case.

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Author information

Correspondence to P. Jean-Jacques Herings.

Additional information

E. Grigorieva acknowledges support by the Dutch Science Foundation NWO through grant 401-01-101. P.J.J. Herings acknowledges support by the Dutch Science Foundation NWO through a VICI grant. R. Müller acknowledges support by European Commission through funds for the International Institute of Infonomics.

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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Grigorieva, E., Herings, P.J., Müller, R. et al. On the Fastest Vickrey Algorithm. Algorithmica 58, 566–590 (2010). https://doi.org/10.1007/s00453-009-9285-4

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Keywords

  • Single item auctions
  • Vickrey-Clarke-Groves implementation
  • Algorithms
  • Performance analysis