All equilibria of the multi-unit Vickrey auction

Andreas Blume, Paul Heidhues, Jonathan Lafky, Johannes Münster, Meixia Zhang

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


This paper completely characterizes the set of equilibria of the Vickrey auction for multiple identical units when buyers have non-increasing marginal valuations and there are at least three potential buyers. There are two types of equilibria: In the first class of equilibria there are positive bids below the maximum valuation. In this class, above a threshold value all bidders bid truthfully on all units. One of the bidders bids at the threshold for any unit for which his valuation is below the threshold; the other bidders bid zero in this range. In the second class of equilibria there are as many bids at or above the maximum valuation as there are units. The allocation of these bids is arbitrary across bidders. All the remaining bids equal zero. With any positive reserve price equilibrium becomes unique: Bidders bid truthfully on all units for which their valuation exceeds the reserve price.

Original languageEnglish (US)
Pages (from-to)729-741
Number of pages13
JournalGames and Economic Behavior
Issue number2
StatePublished - Jul 2009


  • Core
  • Ex-post equilibrium
  • Multi-unit auction
  • Reserve price
  • Uniqueness
  • Vickrey auction

ASJC Scopus subject areas

  • Finance
  • Economics and Econometrics


Dive into the research topics of 'All equilibria of the multi-unit Vickrey auction'. Together they form a unique fingerprint.

Cite this