Inefficiency of equilibria in digital mechanisms with continuous valuations
A digital mechanism is defined as an iterative procedure in which bidders select an action, from a finite set, in each iteration. When bidders have continuous valuations and make strategic reports, we show that any ex post implementation of the Vickrey choice rule via such a mechanism needs infinitely many iterations for almost all realizations of the bidders’ valuations. Thus, when valuations are drawn from a continuous probability distribution, the Vickrey choice rule can only be used at the expense of a running time that is infinite with probability one. This infeasibility result even holds in the case of two bidders and the Vickrey choice rule only being required to be established with probability one. Establishing the efficient allocation when the n bidders’ report truthfully contrasts starkly to the previous setting: a bisection procedure has a finite running time almost always, and an expected number of reports are equal to 2n. Using a Groves payment scheme rather than Vickrey’s second price payment scheme somewhat mitigates the problem. We provide an example mechanism with a Groves payment scheme, in which the running time of the mechanism in equilibrium is finite with probability 12.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 47 (2011)
Issue (Month): 4-5 ()
|Contact details of provider:|| Web page: http://www.elsevier.com/locate/jmateco|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Grigorieva, Elena & Jean-Jacques Herings, P. & Müller, Rudolf & Vermeulen, Dries, 2012.
"Fraction auctions: The tradeoff between efficiency and running time,"
European Journal of Operational Research,
Elsevier, vol. 220(2), pages 577-587.
- Grigorieva Elena & Herings P. Jean-Jacques & Müller Rudolf & Vermeulen Dries, 2009. "Fraction auctions: the tradeoff between effciency and running time," Research Memorandum 045, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
- Green, Jerry & Laffont, Jean-Jacques, 1977. "Characterization of Satisfactory Mechanisms for the Revelation of Preferences for Public Goods," Econometrica, Econometric Society, vol. 45(2), pages 427-438, March.
- Rothkopf, Michael H. & Harstad, Ronald M., 1994. "On the role of discrete bid levels in oral auctions," European Journal of Operational Research, Elsevier, vol. 74(3), pages 572-581, May.
- Fadel, Ronald & Segal, Ilya, 2009. "The communication cost of selfishness," Journal of Economic Theory, Elsevier, vol. 144(5), pages 1895-1920, September.
- William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, 03.
- Groves, Theodore, 1973. "Incentives in Teams," Econometrica, Econometric Society, vol. 41(4), pages 617-631, July. Full references (including those not matched with items on IDEAS)